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The Fitted Finite Volume and Power Penalty Methods for Option Pricing Song Wang
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To Phyllis Sternberg Perrakis (July 1941–March 2018), literary scholar, editor, teacher, but also lover, wife, mother and grandmother. She encouraged me to write this book but was not there when it was finished.
Foreword
Stylianos Perrakis is a distinguished and prolific economist with broad interests in industrial organization, labor economics, policy, regulation, and, above all, stochastic dominance, financial engineering, transaction costs, and derivatives pricing. Perrakis is one of the pioneers in the systematic exploration of the fundamental concept of stochastic dominance as applied to the pricing of options and has brought it to the forefront of economic inquiry with important theoretical and empirical contributions. Perrakis is eminently qualified to present a systematic development of the theory of stochastic dominance and bring in one volume its theoretical and empirical applications to the pricing of options.
Second-order stochastic dominance describes the shared preferences of all risk-averse investors, irrespective of their particular utility functions and strength of aversion to risk, in the ordering of gambles. In comparing two same-cost portfolios, if portfolio A stochastically dominates in secondorder portfolio B, then an investor increases her expected utility by shifting her investment from portfolio B to portfolio A irrespective of her particular increasing and concave utility function. The strength of stochastic dominance lies in its universality across all risk-averse investors, given that investors have heterogeneous preferences, but it is credible to assume that these preferences describe investors that are averse to risk.
This book commences with an introduction to the theory of stochastic dominance and proceeds to the application of stochastic dominance to the pricing of options. Specifically, the theory of stochastic dominance provides bounds to the prices of options or, more generally, to the prices of option portfolios: portfolios that judiciously incorporate options that
violate these bounds stochastically dominate portfolios that exclude them. At the continuous time limit, the single option bounds converge to the corresponding Black-Scholes-Merton option prices in the case of diffusion processes and provide useful tight bounds in the case of mixed jumpdiffusion processes.
In the next stage, Perrakis addresses the more realistic case that incorporates costs in trading the options and the underlying assets. The theory is brought to the data demonstrating in out-of-sample tests that portfolios that incorporate options that violate these bounds stochastically dominate portfolios that exclude them, net of transaction costs. Perrakis writes with authority as he is a major contributor to both the theory and its empirical applications. In the concluding section, Perrakis outlines future applications of stochastic dominance.
I have had the privilege of being a long-time collaborator of Perrakis in his lifelong journey of applying stochastic dominance to the pricing of options and I invite the reader to participate in this exciting journey.
Leo Melamed Professor of Finance
The University of Chicago Booth School of Business Chicago, IL, USA
George M. Constantinides
PreFace
This book addresses itself primarily to economists, financial engineers and mathematicians interested in theoretical models of financial derivatives that have empirical and practical implications. Its basic methodology employs the economic concept of stochastic dominance, a concept that was introduced more than 50 years ago in a different context, in order to explore some little-noticed elements of one of the most dynamic areas of finance, the valuation of options. The research that underlies it took place over a period of almost 40 years, starting in 1980 and continuing till now, with some of the most interesting contributions appearing during the last decade. The unified treatment that is presented here highlights its empirical significance, which has not been exhausted yet. Several potential research projects arising from its theoretical component are described in individual chapters.
This monograph pulls together in an integrated framework the entire theory of option pricing under stochastic dominance, first in a frictionless world and then in the presence of proportional transaction costs. It reviews the existing published results, some of which are in less well-known publications, and completes them by presenting unpublished work by the author, on its own or with co-authors. It compares stochastic dominance with alternative approaches to the study of options and indicates the strengths, as well as the limitations, of the approach.
A one-sentence summary of the difference between stochastic dominance and the alternative approaches to option pricing that arose out of dynamic asset pricing theory is that the former is data-driven while the latter is model-based. This summary does not do justice to either approach:
there are rigorous models in stochastic dominance and there is a large volume of empirical option market work in dynamic asset pricing. Nonetheless, dynamic asset pricing accepts as given the efficiency of financial markets and evaluates the data in the context of specific asset pricing models. Stochastic dominance has developed models that rely on the data to determine whether option markets are efficient.
In at least two cases, the practical applications of the theory presented here extend beyond the narrow world of financial theoreticians focused on asset pricing and cover portfolio managers and financial engineers working for the insurance industry. The first case is the valuation of options in the presence of rare events, for which the alternative theory of arbitrage equilibrium has not been particularly successful, a fact that has caused a prominent researcher to characterize the valuation of rare event risk as a “dark matter of finance”.1 This failure is particularly important in valuing bonds with embedded options indexed on catastrophe events, such as hurricanes, floods, earthquakes and so on. As indicated in Chap. 2, such instruments are traded infrequently over the counter, and the observed prices have varied widely in ways that make no sense in the traditional no arbitrageequilibrium approach of dynamic asset pricing theory. Stochastic dominance allows us to value them consistently given the frequency and intensity of the underlying physical event. This advantage is bound to become more important in view of the fact that these physical events will be affected in predictable ways by the forthcoming climate changes long before reliable prices for the financial instruments indexed on them can be observed.
The second practical application of stochastic dominance is of interest to all portfolio managers and not just those who work in insurance. In Chap. 4, stochastic dominance is used to derive bounds on index options in the presence of proportional transaction costs in the underlying market, and in Chap. 5, the methodology is applied in order to identify mispriced individual options and option portfolios, and assess the benefits of exploiting these mispricings for trading purposes. For the S&P 500 index and short-term options, these mispriced portfolios translate into a major increase of the expected returns on the index, which is achieved by combining it with the suitably chosen mispriced portfolio. Since the S&P 500 index is arguably the most important benchmark for any managed portfolio, the importance of stochastic dominance for portfolio management does not need any further demonstration.
1 See Ross (2015, p. 616).
As already noted, the original idea of applying the theoretical concept of stochastic dominance to option pricing was conceived around 1980, although the first article did not appear till 1984. Recall that at that time, about ten years after the publication of the seminal Black and Scholes (1973) and Merton (1973) papers, the study of option markets was in full bloom, producing pioneering extensions of the original paradigm along several dimensions that enriched it and made it suitable for empirical explorations of option pricing and theoretical applications to other domains. An incomplete list of these extensions includes Merton (1976) and Cox and Ross (1976), who expanded the asset dynamics of the original articles. Cox, Ross and Rubinstein (1979) and Rendleman and Bartter (1979) introduced the binomial model and bridged the gap between discrete and continuous time option pricing, while Rubinstein (1976), Breeden (1979) and Harrison and Kreps (1979) presented integrated capital market equilibrium models that made possible the valuation of contingent claims on traded assets. Several terms associated with these models became standard in the vocabulary of graduate student training relating to options: no arbitrage equilibrium, complete and incomplete markets, pricing kernel, martingales, risk-neutral distributions and so on.
In a world without the frictions that transaction costs represent the new theory did not solve any problems for which solutions did not already exist within the familiar continuous time simultaneous equilibrium and no arbitrage framework. In this frictionless world, the stochastic dominance approach leads to an alternative derivation of the Black–Scholes–Merton option price for index options under generalized diffusion asset dynamics, a fact that was already known in the 1980s but did not appear in rigorous form till 2014. It also provides an alternative option valuation model in the presence of rare event risk that avoids some of the pitfalls of the equilibrium model. Further, in that same frictionless world, it is possible to extend the derivation to equity options, in a formulation that relies on a capital market equilibrium that links the index and the equities but does not require either weak aggregation or a representative investor.
While these frictionless results are of theoretical interest and have had no empirical applications so far, the contributions of stochastic dominance to option valuation in the presence of proportional transaction costs are fundamental, since there is no obvious alternative to them and they have been shown to be empirically important. The extension of the basic stochastic dominance methodology to the world with frictions represented by proportional transaction costs in the underlying asset was done at the
end of the 1990s. I am indebted to George Constantinides, the acknowledged world leader in portfolio selection under transaction costs, whose collaboration was indispensable for the extension of the methodology to option pricing under such conditions. This extension took place after I became aware of the limitations of the traditional no arbitrage approach in such a setting, to which I had already contributed several articles extending it to American options even though it was obvious that the derived results were collapsing into triviality as the frequency of trading increased. This monograph summarizes all meaningful existing option pricing results derived by stochastic dominance in that same setting, mentioning also those cases where the method does not work and new results are needed as in, for instance, equity options.
It also underlines the fact that this approach is the only one that has been tested empirically in its implications in a realistic setting. Note that the index option market is characterized by very wide bid-ask spreads for outof-the-money options, especially for shorter (one month or less) maturities. Nonetheless, these options are not only extremely liquid but also form the basis for the VIX volatility index and for many, if not most, empirical studies of integrated underlying and option market equilibrium in a frictionless world. The paucity of empirical work in the realistic world of bid-ask spreads in the option market is striking, in view of the proliferation of empirical studies in the frictionless world, where the equilibrium values are not observable in that market while the observable bid-ask spreads are the proverbial elephant in the room that everyone ignores. It becomes even more so in view of the fact that the empirical studies that have appeared using stochastic dominance, in all of which Constantinides and myself were co-authors, documented widespread tradable anomalies in the option market that involved out-of-the-money but still very liquid options.
Considerable space is also devoted to issues that stochastic dominance has not been able to tackle so far in both the frictionless world and under proportional transaction costs—at least not by those who have devoted time mastering it. Most important among them is its inability to accommodate multiple state variables, such as time-varying volatility, which is an undeniable feature of financial markets. Although its empirical importance in the pricing of short-term options is probably low and does not affect the mispricing results, the forward-looking volatility statistics extracted from an option market cross-section do convey useful information, as we shall see in Chaps. 5 and 6. For this reason, an integrated model of simultaneous equilibrium that recognizes the time-varying nature of volatility and the bid-ask spreads in both markets is a worthwhile project.
As I make it clear in the course of the text, in addition to Constantinides I am also indebted to several colleagues whose methodological contributions have enriched my own understanding of the topic and allowed me to extend its applications to new domains. No one who uses the term “stochastic dominance” can ignore the fundamental work that Haim Levy and his associates have done over the years in the realm of portfolio selection, which was transferred with little reformulation into the pricing of options. Peter Ritchken, on his own or with co-authors, exploited the linkage of stochastic dominance with the implied monotone decreasing pricing kernel and contributed the linear programming approach to deriving option bounds, which relies heavily on the convexity of the option prices with respect to the price of the underlying asset. Jens Jackwerth was instrumental in designing the first empirical application, which also attempted to expand the pricing kernel monotonicity to the pricing of an entire cross-section of options in the presence of transaction costs. Peter Ryan co-authored with me in 1984 the first article on option pricing bounds that is still relevant today as a foundation for empirical work after its extension to incorporate transaction costs. Last, I am indebted to my long-time collaborators and former students Michael Oancea, Michal Czerwonko, Ali Boloorforoosh and Hamed Ghanbari, who have coauthored fundamental methodological studies in the topic and have contributed, respectively, advanced mathematical insights and numerical skills that I do not possess. Czerwonko is also acknowledged as a co-author on a chapter of this book, which breaks new ground in identifying entire cross-sections of bounds for efficient option prices in a world of transaction costs. Needless to say, I remain solely responsible for any errors or omissions.
Montreal, QC, Canada Stylianos Perrakis
reFerences
Black, F., and M. Scholes. 1973. The Pricing of Options and Corporate Liabilities. Journal of Political Economy 81: 637–654.
Breeden, Douglas. 1979. An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities. Journal of Financial Economics 7: 265–296.
Cox, J.C., and S.A. Ross. 1976. The Valuation of Options for Alternative Stochastic Processes. Journal of Financial Economics 3: 145–166.
Cox, J.C., S.A. Ross, and M. Rubinstein. 1979. Option Pricing: A Simplified Approach. Journal of Financial Economics 7: 229–263.
Harrison, J.M., and D. Kreps. 1979. Martingales and Arbitrage in Multiperiod Securities Markets. Journal of Economic Theory 20: 381–408.
Merton, R.C. 1973. Theory of Rational Option Pricing. Bell Journal of Economics and Management Science 4: 141–84.
Rendleman, R.J., and B.J. Bartter. 1979. Two-State Option Pricing. Journal of Finance 34: 1093–1110.
Ross, S. 2015. The Recovery Theorem. Journal of Finance 70: 615–648.
Rubinstein, Mark. 1976. The Valuation of Uncertain Income Streams and the Pricing of Options. Bell Journal of Economics 7: 407–425.
Fig. 1.1
List oF Figures
Fig. 1.2
Second-degree stochastic dominance for single crossing distributions When two distributions cross only once at point D then a sufficient condition for FG 2 is that Area (A) ≥ Area (B), which also implies that the mean of Fx() is greater than or equal to the mean of Gx() 6
Second-degree stochastic dominance for distributions crossing twice When two distributions cross at two points then it is no longer sufficient for FG 2 that the mean of Fx() is greater than or equal to the mean of Gx() . We must also have Area (A) ≥ Area (B), and the two conditions are not equivalent 7
Fig. 1.3
Fig. 1.4
Second-degree stochastic dominance for single crossing functions of a random variable
If X is a random variable and HX() a single crossing function as shown, with respective distributions Gx Fx () () and then a sufficient condition for FG 2 is that EH XE X ()
≥ [] 8
Second-degree stochastic dominance for functions of a random variable that cross twice
If X is a random variable and HX() a function crossing twice as shown, with respective distributions Gx Fx () () and then a sufficient condition for FG 2 is that
Fig. 2.1 The convex hull czjj ˆ () and the option bounds
The graph shows the function
plotted against
for jn =… 1, , . The call option bounds are at the intersections of the convex hull with the vertical line from the riskless rate of return R −1
Fig. 2.2 Convergence of the option bounds to the common BSM value for a lognormal diffusion
The figure illustrates the convergence of the three-month at-the-money call option upper and lower bounds as the number of time partitions increases, for three different values of the instantaneous mean of the diffusion process. The remaining parameters are as shown in the figure
Fig. 2.3 Convergence of the option bounds to their final values for a jump-diffusion process
The graphs show the convergence of the upper and lower bounds for the price of a three-month at-the-money call option as the number of time partitions increases for a jump-diffusion process. The jump amplitude distribution is lognormal, truncated to a worst case of −20%. The upper line shows the upper bound under no truncation. The parameters of the process are SK r jj == == == =− = 100 42 20 06 0057 ,%,%,%,. ,. ,%
Fig. 2.4 Values of the relative risk aversion coefficient consistent with the option bounds
The dark blue curve in the figure shows the values of the relative risk aversion coefficient γ consistent with equilibrium option prices equal to each value within the interval between the jump-diffusion bounds for the three-month at-the-money call option shown in Fig. 2.3, found by solving the system (2.59) and (2.60)
Fig. 2.5 Bounds for a CAT reinsurance contract with a ceiling and a deductible
The dark line is the single period conditional payoff function CH Ti i () of the hurricane reinsurance contract as a function of the conditional landed hurricane intensity, defined as HE HH H ij ji=≥
and
in = 01,, .., . The bounds are at the intersection points of the convex hull containing the payoff function with the vertical line from the value F of the futures contact indexed on hurricane intensity
33
39
55
60
75
Fig. 4.1 The upper and lower bounds for a call option given by Theorems 1, 3 and 4
The figure shows the upper bound of Theorem 1 and the lower bound of Theorem 3 at its continuous time limit as in Theorem 4 under diffusion, for the indicated values of the transaction cost parameter and for all degrees of moneyness. The parameters are as follows: K = 100 , σ = 20% , µ = 8% , r = 4% , T = 30 days
Fig. 4.2 Convergence of the call lower bound to its continuous time limit under diffusion
The figure displays the convergence behavior of the Theorem 3 lower bound (4.19) to its continuous time diffusion limit given by Theorem 4 and derived for the uniform distribution of the discrete time stock returns (4.38). The parameters are as follows: K = 100 , σ = 20%, µ = 8%, r = 4% , T = 30 days , k = 05.%
Fig. 4.3 Convergence of the discrete time call lower bound to its continuous time limit
The figure displays the relative convergence errors 1 5 () () CBSM kS / . ϕ , of the Theorem 3 lower bound (4.19) from its continuous time limit under diffusion given by Theorem 4 and derived for the uniform distribution of the stock returns (4.38). The parameters are as follows: K = 100 ,
Fig. 4.4 The convergence of the Theorem 3 call lower bound g-function to its continuous time limit
The figure displays the convergence behavior of the g-function (4.21) to its continuous time limit Nd1 ∗ () , where dd kS 11 ∗ = () () ϕ ,. derived for the uniform distribution of the stock returns (4.38). The parameters are as follows: K = 100 ,
20%
8%
Fig. 4.5 Convergence errors of the g-function for various time partitions
The figure displays the relative convergence errors of the g-function (4.21) from its continuous time limit Nd1 ∗ (), where dd kS 11 ∗ = () () ϕ ,. derived for the uniform distribution of the stock returns (4.38). The parameters are as follows: K = 100 , σ = 20%, µ = 8%, r = 4% , T = 30, k = 05.%
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132
Fig. 5.1 The Constantinides and Perrakis (2002) call option bounds and the observed option prices
This figure reproduces Panels A, B, F and G from CJP (2009, Figs. 1, 3 and 4). It shows the comparisons of the CP bounds and the call option quotes, respectively for the two early subperiods, the pre-October 1987 crash and the immediate post-crash, as well as the two last subperiods of February 2000 to May 2003 and June 2003 to May 2006. Both bounds and observed prices are represented by their respective IV, used here as a translation device, as functions of moneyness expressed as the ratio of strike price to index value. Bid and ask prices are represented by circles and crosses, respectively
Fig. 5.2 Difference in the realized returns between the OT and IT 28- and 14-day portfolios
184
The returns are measured in the 278-, 28- and 14-day periods over January 1990–February 2013 and sorted by the contemporaneous S&P 500 returns. Bars in the graph correspond to means for 100 equally spaced S&P returns. Consistent with the objective of constructing OT portfolios that stochastically dominate the IT portfolios, the difference in returns is generally decreasing in the S&P 500 index return 197
Fig. 6.1 Time series of the difference between P- and Q-volatilities
The figure shows the time series of the difference between the VIX volatility (Q-volatility) index and the observed return volatility over a 30-day period following each VIX observation (P-volatility). The time series has been smoothed as shown 216
Fig. 6.2 Cumulative prospect theory value function
The figure shows the decision-maker’s value function given by Eq. (6.25) according to CPT. The horizontal line shows the changes in payoff or wealth, with the origin of the axis denoting the current situation
245
List oF tabLes
Table 3.1 Average observed S&P 500 index option bid-ask spreads, January 1990–February 2013
The table shows the observed average bid-ask spreads for S&P 500 index options as percentages of their midpoints for two maturities over the period January 1990–February 2013 89
Table 3.2 Continuous time approximations of the NT region for fixed time horizons
The table displays the convergence of the NT region for the indicated investment horizons. The values for buy
and
boundaries derived for a given partition or number of jumps left are followed by the necessary computational time in each case. N/F and N/A denote not feasible and not available respectively. Except for relative risk aversion (RRA), which is equal to 3.5 here, the parameters are as in the Liu-Loewenstein (2002) diffusion base case: σ = 20%, riskless rate of 5%, risk premium of 7% with no cash dividends, transaction cost rate on sales of the risky asset of 1% 104
Table 4.1 American call option upper bound under lognormal diffusion and transaction costs
Upper bounds on the reservation write price of an American call implied by Theorem 5, as functions of the transaction cost rate and the strike-to-price ratio, K/S, under lognormal return distribution. Parameter values: expiration 30 days, annual risk-free rate 3%, annual expected stock return 8%, annual volatility 20% and annual dividend yield 1% 139
Table 4.2
Table 4.3
American call option upper bound under jump diffusion and transaction costs
Upper bounds on the reservation write price of an American call implied by Theorem 5, as functions of the transaction cost rate and the strike-to-price ratio, K/S, under a mixed lognormal-jump distribution. Parameter values: expiration 30 days, annual risk-free rate 3%, annual expected stock return 8%, annual volatility 20%, annual dividend yield 1%, annual jump frequency 1/5, lognormal jump amplitude with mean −1% and volatility 7%
American put option lower bound under lognormal diffusion and transaction costs
Lower bounds on the reservation purchase price of an American put implied by Theorem 6 as functions of the transaction costs rate and the strike-to-price ratio, K/S, under lognormal return distribution. Parameter values: expiration 30 days, annual risk-free rate 3%, annual expected stock return 8%, annual volatility 20% and annual dividend yield 1%
140
143
Table 4.4
American put option lower bound under lognormal diffusion and transaction costs
Lower bounds on the reservation purchase price of an American put implied by Theorem 6, as functions of the transaction costs rate and the strike-to-price ratio, K/S, under a mixed lognormal-jump distribution. Parameter values: expiration 30 days, annual risk-free rate 3%, annual expected stock return 8%, annual total volatility 20%, annual dividend yield 1%, annual jump frequency 1/5, lognormal jump amplitude with mean −1%, and volatility 7%
Table 5.1 Returns of call trader and index trader
Equally weighted average of all violating options equivalent to one option per share was traded at each date. The symbols * and ** denote a difference in sample means of the OT and IT traders significant at the 5% and 1% levels in a one-sided bootstrap test with 9999 trials. Maximal t-statistics for Davidson and Duclos (DD 2000) test are compared to critical values of Studentized Maximum Modulus Distribution tabulated in Stoline and Ury (1979) for three nominal levels of 1, 5 and 10% with k = 20 and ν =∞ . The p-values for HOTIT 02:, which are greater than 10%, the highest nominal level available in Stoline and Ury (1979) tables are not reported here. The p-values for the Davidson and Duclos (2013) test are based on 999 bootstrap trials. The p-values for
are equal to one and are not reported here
144
Table 5.2 Frictionless returns on optimal portfolios and straddles
The table displays in percentage points monthly frictionless excess returns on OT portfolios and straddles as well as 95% bootstrap confidence intervals for market returns. We present results for the entire available sample period, January 1990-February 2013. The symbols *, ** and *** respectively denote statistical significance at the 10%, 5% and 1% level via a bootstrap test with 10,000 draws. The p-values for this test are consistent with bootstrapping t-statistics as in CHJ (2013, Table 2)
Table 6.1 GARCH option prices
Table 6.2 Volatility forecast errors, January 1990–February 2013
The table displays the average bias, root mean square error and mean absolute error for volatility forecast modes. The quantity for which statistics are shown is annualized volatility times 100
Table 6.3 Portfolio returns and stochastic dominance tests in relation to volatility forecast, January 1990–February 2013
The table presents results for the Sharpe ratio portfolio selection criterion. µ is the mean and σOT IT is the volatility of the difference of the annualized percentage return between the IT and OT portfolios. The volatility of the return of the 28-day, 14-day and 7-day IT portfolios is 16.48%, 17.15% and 18.12%, respectively. Statistical test is performed on the basis of the total number of dates. The p-values for the difference in means are derived under via bootstrap with 10,000 draws. For the Davidson and Duclos (DD 2013) test, 10% trimming (deleting sequentially lowest outcomes in either return set) in the left tail is uniformly performed while similar trimming in the right tail is as shown. The results of the DD tests without trimming in the right tail are not shown because they are qualitatively the same as the p-values for the difference in means
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220
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CHAPTER
1
Stochastic Dominance: Introduction
Stochastic dominance (SD) is a concept about choice under risk that was originally derived from the economics literature for the ordering of uncertain prospects by a particular set of investors. This chapter reviews the early definitions and applications which started in 1962 with a contribution in the economics literature by Quirk and Saposnik and expanded into mathematics, finance and possibly other fields as well. In the financial literature it was originally intended to cover portfolio selection, which was dominated till then by the mean-variance model that had been developed ten years earlier in the seminal article by Harry Markowitz (1952).
The importance of SD as a choice criterion is that it is fully non-parametric, insofar as it does not impose any restrictions on the decision-maker’s utility beyond those prescribed by the behavioral axioms that form the basis of traditional utility theory. It also does not limit the distributions of the future states of the basic factor that determines utility, which is usually wealth, income or returns in the problems that we will consider. By contrast, the mean-variance criterion is consistent with expected utility only under the very limited (and unrealistic) case of quadratic utility or, alternatively, with normal distributions of future states.
This chapter is not intended to be a comprehensive review of SD. In particular, it does not survey several well-known contributions that have appeared in the mathematical-statistical literature that have not had any financial applications. It limits itself to its contributions only
S. Perrakis, Stochastic Dominance Option Pricing, https://doi.org/10.1007/978-3-030-11590-6_1
insofar as they have had implications for the study of options. It also pays lip service to efforts to apply the concept to portfolio selection, which have a longer history. Lastly, it reviews the all-important econometric tests of SD between two time series, which have played a major role in validating empirically the SD approach to option pricing.
1.1 Definition
SD is defined by degrees (or orders) depending on the properties of the set of decision-makers as defined by their utility functions. Essentially, it is a mapping from the domain of utilities, generally conceived as functions of consumption or wealth, to the domain of distribution functions defined by their properties. This chapter considers only unidimensional utility functions since these are the only ones with applications to option pricing. Extensions to more than one dimension are discussed in the last chapters as suggestions for further research.
Quirk and Saposnik (1962) developed the concept and criteria for firstdegree stochastic dominance (FSD), which considered the set of decisionmakers whose utility functions are non-decreasing, thus including risk-loving agents. The set was limited to risk-averse decision-makers with concave utility functions in two simultaneous studies by Hadar and Russell (1969) and Hanoch and Levy (1969), the second-degree stochastic dominance (SSD) criteria, which are tighter than the first degree since they refer to a subset of the first-degree decision-makers. Third-degree stochastic dominance (TSD) was developed by Whitmore (1970) and is implied by the decreasing absolute risk aversion (DARA) behavioral property of Arrow (1965) and Pratt (1964). There are also even higher order dominance criteria with restrictions on the shape of the utility functions whose behavioral justifications were developed much later; see, for instance, Eeckhoudt and Schlesinger (2006). These will not be covered here, although their option pricing implications, which to our knowledge have not had any empirical applications, are mentioned briefly in the next chapter.
Let ux() denote the utility function of a random quantity defined on the real line, with ux Ui UU U i () ∈= ⊃⊃ 12 3 12 3 ,, , . By definition we have:
Let also Fx Gx () () and denote two alternative distributions, and denote by FG i i ,, , = 12 3 the dominance relation that Fx() dominates Gx() to the corresponding degree, implying that it is preferred by all decision-makers belonging to the corresponding set. The following relation defines dominance at the corresponding degree:
Further, note that obviously FG FG 12 ⇒ and FG FG 23 ⇒ .
From the definition of the dominance relations (1.2) we get the following ordering of the pair of distributions according to the corresponding criterion, as well as the necessary and sufficient conditions for the corresponding degree of dominance.1 In all cases the necessity is proven by relying on the properties of the utility function, while the sufficiency is established by showing that a utility function violating dominance exists if the conditions do not hold at some point.
fandonlyifforallandforsome () ()
Remarks
(a) For any degree of dominance, the possible outcomes of a comparison of Fx Gx () () and are that FG i , GF i , or that neither one of
1 The presentation of the dominance conditions (1.3a, 1.3b, 1.3c) follows the more general Hanoch and Levy (1969) that defines the domain of the distributions as the entire real line and covers all types of distributions. In practice all our useful results are restricted to the positive real line.
S. PERRAKIS
the two distributions dominates the other. Since the dominance relation is obviously transitive, in any finite set of admissible distributions a distribution becomes automatically part of the dominated or inefficient set, since it is never going to be chosen by a decision-maker of the corresponding utility set. Unfortunately, the above relations can only allow the determination of the undominated or efficient set by rejecting dominance for all pairwise pairings of the distributions that were not found inefficient. For this reason a more informative SSD test is that of the hypothesis FG i , in which case rejection of the null implies dominance of F over G
(b) All degrees of dominance have as a necessary condition that if FG i i ,, , = 12 3 then the mean under F exceeds that under G , or
≥ xdFxdG. Unfortunately, no similar orderings emerge for the higher order moments.2
(c) There are other dominance criteria, equivalent to (1.3a, 1.3b, 1.3c), which have been proposed as more convenient for the solution of specific problems. For instance, the integral relations can be inverted and expressed in terms of the quantiles of the distributions. Similarly, there are dominance conditions applicable to transformations of the original variables represented by the two distributions.3
(d) An important case, originally presented by Levy and Kroll (1978), arises when each one of the two random variables is a risky asset which is also combined with a riskless asset, whose return is lower than the expected returns of the two risky assets. The methodology applied in this case is also used in one of the frictionless SD option pricing studies examined in the next chapter.
(e) Relations (1.3a, 1.3b, 1.3c) are one-period results, referring to the utility of terminal wealth of the two alternative prospects.4 If these prospects are outcomes of specific intermediate actions (e.g. portfolio choices) then the single period assumption is no longer
2 In fact, the classic analysis of risk in Rothschild and Stiglitz (1970) shows that risk comparisons between two distributions are not equivalent to comparisons of their variances.
3 These are presented in the survey article by Levy (1992).
4 Multiperiod SSD rules presented in Levy (2016, Chapter 13) are not practical for option market applications.
acceptable and recursive expressions are required. This is a key feature of all the results in this book.
(f) FSD is too loose a criterion to be of any use in deriving meaningful results. There is, however, one application that will be highlighted in Chaps. 5 and 6 of this text, when it coincides with the so-called single price law of market efficiency. This is the case where two assets that have the same returns under all possible future situations must also have the same price. Hence, if it is possible to replicate the probability distribution of an asset’s future cash flow at some future horizon, for instance by using a portfolio of its derivatives, then the asset and the portfolio should have the same price, otherwise it is possible to derive arbitrage profits. This is a case of FSD: suppose P1 and P2 represent, respectively, the current prices of the asset and the portfolio with PP 12 > , R is the riskless asset return and Fx() the distribution of the payoff at the target date, then the distribution of the net returns are, respectively, Fx PR () 1 and Fx PR () 2 , and the second clearly dominates the first.
(g) SSD is our base case, which will be examined systematically in the next section with respect to its implications for risk and its further properties that will be used in option pricing.
(h) TSD has had important applications in portfolio selection, but its use in option pricing has been limited for technical reasons; it is briefly reviewed in the next chapter.
1.2
Risk anD seconD-DegRee stochastic Dominance
We shall consider distributions in the positive real line and with a bounded support, since these will form the bulk of the cases that will become relevant in many of the theoretical and in all the empirical option pricing applications. Equation (1.3b) implies that Fx() should initially lie below Gx(). If the two don’t cross anywhere then we have FSD of Fx() over Gx(), so we assume that they cross at least once. The two important cases for our purposes are when they cross exactly once and exactly twice, as shown in the two figures below.
In Fig. 1.1 the SSD relation (1.3b) boils down to the area between the two curves indicated by A exceeding the one denoted by B. The difference between the two is equal to the difference between the means of the
Fig. 1.1 Second-degree stochastic dominance for single crossing distributions When two distributions cross only once at point D then a sufficient condition for FG 2 is that Area (A) ≥ Area (B), which also implies that the mean of Fx() is greater than or equal to the mean of Gx()
two distributions, which becomes thus a sufficient condition for SSD under the single crossing property. By contrast, in the double-crossing case shown in Fig. 1.2, the inequality of the means is no longer sufficient for SSD: the difference in means is equal to A + C – B, but SSD exists only if A – B > 0. The location of the second crossing point E becomes, therefore, crucial in establishing SSD.
The relation FG 2 , if it can be established, implies that Fx() has an equal or higher mean than Gx() and a lower risk. If risk is not represented by variance then we need an alternative definition of it. This was discussed at length by Rothschild and Stiglitz (1970) who included two other definitions of risk, in addition to the definition (1.2) that every risk averter prefers Fx() to Gx() . 5 The first one was that Fx() was the distribution of a random variable X , while Gx() represented the variable X + ε, where EX ε = 0 for all X . The second one considered meanpreserving spreads, namely the cases in which Fx Gx () () and had the same mean but Gx() was obtained from Fx() by shifting probability
5 Another definition involving the risk premium necessary to subtract from the mean of the risky prospect to represent expected utility was shown to be equivalent to the others; see Levy (2016, Chapter 8).
Fig. 1.2 Second-degree stochastic dominance for distributions crossing twice When two distributions cross at two points then it is no longer sufficient for FG 2 that the mean of Fx() is greater than or equal to the mean of Gx() . We must also have Area (A) ≥ Area (B), and the two conditions are not equivalent
weights from the center toward the tails, chosen so that the mean stayed the same. These are also important in our applications, even though they are not always consistent with (1.2) when transaction costs are included.
The single crossing case of SSD shown in Fig. 1.1 is more informative if we map the distributions Fx Gx () () and in the domain of terminal values of a function HX() and of X respectively, which obviously must intersect at a single point as shown in Fig. 1.3, corresponding to Point D in Fig. 1.1. Figure 1.4 shows the similarly mapped Fx Gx () () and distributions in Fig. 1.2, and Point J that corresponds to Point E in that figure. These two figures, combined with the fact that ′ ()ux is non-increasing for ux U () ∈ 2 , form the basis of the entire approach to option pricing presented in this book. Thus, for the case shown in Fig. 1.3, if X represents terminal wealth or return on investment and HX() an alternative portfolio possibly involving options then the latter shifts the returns from the high to the low states, thus increasing utility, provided the overall expectation inequality EH XE X ()
≥ [] holds, consistent with the definition of risk.
Fig. 1.3 Second-degree stochastic dominance for single crossing functions of a random variable
If X is a random variable and HX() a single crossing function as shown, with respective distributions Gx Fx () () and then a sufficient condition for FG 2 is that EH XE X ()
≥ []
Similarly, in Fig. 1.4 a sufficient condition that FG 2 given the double-crossing property is that EH xx xJ () −≤ ≥ 0, a condition significantly easier to establish than the definition (1.3b).
Important extensions of the definitions of risk were achieved in the special case where a riskless asset can be combined with the two prospects, as noted in the previous section. If the means of the two risky prospects X and Y exceed the riskless return then it is possible to form portfolios of the risky and riskless assets that have equal means. Indeed, if R denotes
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9. Resoglas and Trolitul: United States imports for consumption, 1933-37
10. Synthetic resins classified under paragraph 11: United States imports for consumption, 1931-37
11. Vinyl acetate resins: United States imports for consumption, 1934-37
12. Mowilith resins: United States imports for consumption, 1932-37
13. Synthetic resins: United States
14. Comparison of the international trade of the United States in synthetic resins and in certain raw materials for resins, 1934-37
15. Tariff classification and rates of duty in Tariff act of 1930 upon certain articles made of synthetic resin
16. Manufactured articles n. s. p. f. in which synthetic resin is the chief binding agent: United States imports for consumption, 1931-37
28. Synthetic resins: French imports, by types, and countries, 1931 and 1933-37
29. Synthetic resins: French exports, 1931 and 1933-37 82
30. Manufactures of tar-acid resins: Production in Japan, 1929-35 84
31. Prices of gums and resins in the Netherlands, 1936 86
32. Synthetic resins: Netherland imports by countries 1931 and 1933-37 86
33. Crude naphthalene: United States production, 1918-37 88
34. Refined naphthalene: United States production and sales, 1917-37 89
35. Naphthalene (all grades): World production, by countries, 1933 and 1935 90
36. Naphthalene: German production, imports, exports, and apparent consumption, 1928-37 92
37. Naphthalene: Production in Great Britain, in specified years 92
38. Naphthalene: Exports from the United Kingdom, 192836 93
42. Naphthalene: Rates of duty upon imports into the United States, 1916-38 95
43. Crude naphthalene (solidifying at less than 79° C.): United States imports for consumption, 1919-37 96
44. Refined naphthalene (solidifying at or above 79° C.): United States imports for consumption, 1919-37 96
45. Crude naphthalene (solidifying under 79° C.): United States imports for consumption from principal sources, in specified years 97
46. Crude naphthalene: United States production, imports, and apparent consumption, in specified years 98
47. Phthalic anhydride: United States production and sales, 1917-37 100
48. Glycerin: United States production, 1919-37 103
49. Glycerin: United States production for sale, 1919-35
50. Glycerin: Imports and exports of principal countries, 1931 and 1933-37
51. Glycerin: United States imports for consumption, 191920 and 1923-37
52. Crude glycerin: United States imports for consumption from Cuba, 1919-37 107
53. Crude glycerin: United States imports for consumption from Philippine Islands, 1925-37 107
54. Glycerin: United States exports, 1919-37 108
55. Refined glycerin: United States production, imports, exports, and apparent consumption, in specified years 108
56. Tar acids: Commercial and chemical names, boiling points, and average percent in coal tar 109
57. Tar acids available in coal tar produced and distilled in 1936 110
58. Phenol: Estimated consumption by industries, 1936-37 111
59. Phenol: United States production and sales, in specified years, 1918-37 112
60. Phenol: Estimated annual production, by countries, 1933-35 113
61. Phenol: Rates of duty upon imports into the United States, 1916-37 114
62. Phenol: United States imports for consumption, 191037 115
63. All distillates of tar yielding below 190° C., an amount of tar acids equal to or more than 5 percent: United States imports for consumption, 1918-37 115
64. Phenol: United States exports, 1918-24 116
65. Phenol: United States exports, 1934-36 116
66. Phenol: United States production, imports, exports, and apparent consumption, in specified years, 1918-37 117
67. Meta, ortho, and para cresols: United States production 120
and sales, 1934
68. Refined cresylic acid: United States production and sales, 1929-37 121
69. Cresol: German production, in specified years 122
70. Cresol: German imports and exports in specified years 122
71. Cresol: Production in Czechoslovakia in specified years 123
72. Cresylic acid: British exports, by countries, 1933-37 123
73. The cresols: Rates of duty upon United States imports, 1916-37 124
74. Cresylic acid: Rates of duty upon United States imports, 1916-37 125
75. Metacresol, orthocresol, and paracresol, 90 percent or more pure: United States imports for consumption, 1920 and 1923-37 125
76. Metacresol: United States imports for consumption by principal sources, in specified years 126
77. Orthocresol: United States imports for consumption by principal sources, in specified years 127
78. Paracresol: United States imports for consumption by principal sources, in specified years 128
79. Crude cresylic acid: United States imports for consumption, 1924-37 129
80. Refined cresylic acid: United States imports for consumption, in specified years, 1919-37 129
81. Crude cresylic acid: United States imports for consumption by principal sources, in specified years, 1929-37 130
82. Refined cresylic acid: United States imports for consumption by principal countries, in specified years 130
83. The cresols: Comparison of production and imports, 1934
84. Formaldehyde: United States production and sales, in specified years
85. Formaldehyde: United States exports to principal markets, in specified years
86. Hexamethylenetetramine: United States production and sales, 1923 and 1925-37
87. Hexamethylenetetramine: United States imports for consumption, 1923-37
88. Urea: United States imports for consumption, 1919-20 and 1923-37
89. Urea: United States imports for consumption, by countries, 1931 and 1933-37
90. Thiourea: United States imports through the New York customs district, 1931-37 140
91. Vinyl acetate, unpolymerized: United States imports for consumption, 1931-37
92. Naphthalene: German imports and exports, by countries, 1929 and 1932-37
93. Crude naphthalene: Belgian imports and exports, 193237 146
94. Refined naphthalene: Belgian imports and exports, 1932-37
95. Crude and refined naphthalene: Netherland imports and exports, by countries, 1929 and 1932-37 148
96. Refined naphthalene: Canadian imports, by countries, 1928-29 and 1932-37 150
97. Naphthalene: Japanese imports by countries, 1928-29 and 1932-36 150
98. Crude glycerin: United States imports for consumption, by countries, 1929 and 1931-37
99. Refined glycerin: United States imports for consumption, by countries, 1929 and 1931-37
ILLUSTRATIONS
ACKNOWLEDGMENT
In the preparation of this report, the Commission had the services of Paul K. Lawrence, Prentice N. Dean, and others of the Commission’s staff.
1. INTRODUCTION
This survey deals with the several commercially important types of synthetic resins covered by paragraphs 2, 11, and 28 of the Tariff Act of 1930 and with the raw materials necessary for their production. It is made under the general investigatory powers of the Tariff Commission as provided in section 332 of that act.
The field of synthetic resins is a comparatively new one, most of its commercial development having occurred within the past 10 years. In 1937 the domestic output was more than 160 million pounds as compared with slightly more than 10 million pounds in 1927.
The first important patents on synthetic resins were granted about 25 years ago. These patents covered phenolic resins probably intended for use as substitutes for certain natural resins. It was soon found that these synthetics offered possibilities of application vastly greater than the natural materials. At first progress in their application was slow as is usually the case with new products. During the World War the shortage of phenol promoted interest in the use of the other tar acids as raw materials for synthetic resins and intensive research developed resins from the cresols and higher boiling tar acids. These resins possessed properties sufficiently different from those made from phenol to establish them permanently.
In the meantime research on other types of resins was carried on in the United States and in Europe. The tar-acid resins for molding were the only commercially important ones on the market until about 1929. About that time, however, new commercial products began to appear rapidly Cast phenolic resins became available as material for novelties of unusual brilliancy and beauty, the urea resins to meet the requirements for light colored thermosetting resins in molded articles, and the alkyd resins for use in new surface coatings which replaced conventional paint materials.
Later there followed a number of thermoplastic materials offering new and unusual properties. Vinyl resins found application in molded products and in safety glass. The acrylate resins became the nearest approach to organic glass yet developed. The polystyrene resins, long in the research stage, made their commercial appearance in 1937. Resins from petroleum, from furfural, from adipic acid, and from aniline are on the market. Many others are under investigation and some of them will undoubtedly become important.
The versatility of synthetic resins is most unusual. In various uses they have successfully displaced glass, wood, metal, hard rubber, bone, glue, cellulose plastics, protein plastics, and conventional paint materials. They compete with glass in shades and reflectors and offer properties which will increase their use for this purpose. Cases for scales, radios, and clocks, formerly of wood and metal, are now made of these synthetic resins.
Scope and purpose.
This survey deals with the synthetic resins, the nature and trade in the raw materials necessary for their production, the processes by which they are made, trade in them in the United States and between nations, and the nature of the competition which they meet. It does not go into the details of manufacture of and trade in the multitude of articles made of synthetic resins but stops at the point where these materials are turned over to the resin fabricator. The synthetic resins are but one of four broad groups of organic plastics. The others—natural resins, cellulose ethers and esters, and protein plastics—are discussed herein only as they relate to or compete with the synthetic resins.
The purpose of the survey is to bring together in one publication the available information on synthetic resins so as to provide a basis for consideration of future tariff problems. Because the industries involved are comparatively young and are expanding rapidly, their present day importance is not generally realized. The rapidity with which the synthetic resin industry is developing causes any comprehensive report on the subject to be practically out of date before it can be published. Notwithstanding the progress made each year in the quantity of production, new applications, and new commercial products, the industry may be said to be still in the industrial nursery. This circumstance necessarily limits the period during which any treatment of the subject will be representative.
Fundamental definitions.
The scope of this report has been stated to include synthetic resins up to the point where they are further manufactured, and the raw materials used in producing them It was also stated that natural resins and synthetic plastics other than resins, such as the cellulose compounds and modified rubber compounds, are excluded. The boundaries of these categories are therefore important.[1]
The term “resin” was formerly applied exclusively to a group of natural products, principally of vegetable origin, although at least one important resin, shellac, is of animal origin.[2] These natural resins are widely used in paints, varnishes, and lacquers for decorative and protective surface coatings. They also have extensive use in textile impregnation, adhesives, soap, paper, and in cold-molded articles. In recent years the natural resins have had to compete with synthetic products, and each gravitates toward uses which demand the quality or combination of qualities which it can most completely supply
A resin may be defined as a semisolid or solid, complex, amorphous mixture of organic compounds with no definite melting point and no tendency to crystallize. The resins are characterized by a typical luster and a conchoidal fracture rather than by definite chemical composition. The term includes natural resins, such as colophony (ordinary rosin), copal, damar, lac, mastic, sandarac, shellac, etc., sometimes called gums or gum resins although none of them are true gums.
A synthetic resin is a resin made by synthesis from nonresinous organic compounds. The term includes materials ranging from viscous liquids to hard, infusible, amorphous solids. As a rule synthetic resins possess properties distinct from those of natural resins. The term “plastics,” sometimes applied to synthetic resins, also includes many materials which are not resins.
A plastic is anything possessing plasticity; that is, anything which can be deformed under mechanical stress without losing its coherence or its ability to keep its new form. According to this definition the term includes such materials as putty, cement, clay, glass, and metals, as well as certain modified natural or semisynthetic products, such as cellulose acetate, cellulose nitrate, and casein more commonly so designated. To speak of the plastics industries is almost meaningless because of their enormous scope, including as they do those producing cement, ceramics, confectionery and rubber, as well as those producing the semisynthetic products mentioned.
The resin industry embraces two main types of materials, thermoplastic and thermosetting. Thermoplastic materials are those which, although rigid at normal temperatures, may be deformed and molded under heat and pressure. Among such materials are the cellulose esters, acrylate resins, vinyl resins, polystyrene resins, etc. The recent development of injection molding has given thermoplastics a new significance.
Thermosetting substances are thermoplastic at some stage of their existence, but become hard, rigid, and permanently infusible upon the application of the proper heat and pressure. They are then irreversible whereas the thermoplastics are reversible. Outstanding among the thermosetting resins are tar-acid resins, urea resins, and the alkyd resins.
Tariff history.
The earliest mention of synthetic resins in the tariff laws of the United States was the provision in group III of the Emergency Tariff Act of 1916 for a duty of 30 percent ad valorem and 5 cents per pound on synthetic phenolic resins. None of the non-coal-tar synthetic resins were specifically mentioned prior to the Tariff Act of 1930.
The Tariff Act of 1922 (par. 28) provided for synthetic phenolic resin and all resinlike products, solid, semisolid or liquid, prepared from phenol, cresol, phthalic anhydride, coumarone, indene, or from any other article or material provided for in paragraph 27 or 1549. The rate of duty was 60 percent ad valorem based on American selling price or United States value and 7 cents per pound, with a provision that the ad valorem rate should be reduced to 45 percent 2 years after the passage of the act.
The Tariff Commission made two investigations of synthetic resins under section 316 of the act of 1922. The first was undertaken April 16, 1926, upon complaints of several domestic manufacturers, of unfair methods of competition and unfair acts in the importation and sale of synthetic phenolic resin, Form C, and articles made wholly or in part therefrom, in infringement of the patent rights of the Bakelite Corporation. Following the investigation, the Commission recommended on May 25, 1927, that this material (as described under United States Patents No. 942,809 and 1,424,738) be excluded from entry into the United States. Importers appealed from the findings of the Commission to the Court of Customs Appeals, and the judicial proceedings were ended on October 13, 1930, by denial of a writ of certiorari for the Supreme Court of the United States to review the judgment of the Court of Customs and Patent Appeals. The latter court had held, among other things, that there was substantial evidence in support of each finding of the Commission. On November 26, 1930, the Treasury Department issued an order prohibiting the importation of synthetic phenolic resin, Form C, with certain exceptions. (T. D. 44411.)
The second investigation by the Tariff Commission was instituted on December 23, 1927, also under section 316 of the act of 1922. It concerned unfair methods of competition and unfair acts in the importation into the United States of laminated products of paper or other materials and insoluble, infusible condensation products of phenols and formaldehyde. The Commission recommended to the President that, until March 4, 1929, inclusive, certain products covered by United States Letters Patent Nos. 1,018,385, 1,019,406, and 1,037,719 be excluded from entry into the United States. These products were laminated cloth, paper or the like, combined with
insoluble, infusible condensation products of phenols and formaldehyde. The order of the President prohibiting the importation was contained in T. D. 42801 issued June 11, 1928.
Under the Tariff Act of 1930, practically no changes were made in the provisions of paragraph 28 that concern coal-tar synthetic resins. Paragraph 2 was extended to include, among other things, the resins (polymers) of certain organic compounds. The only commercial products covered by this provision are the vinyl resins. The rate of duty was 30 percent ad valorem on foreign value and 6 cents per pound. Under the trade agreement with Canada, the duty on vinyl acetate, polymerized or unpolymerized, and on synthetic resins made in chief value therefrom was reduced to 15 percent ad valorem and 3 cents per pound (effective Jan. 1, 1936).
The Tariff Act of 1930 contains a provision, in paragraph 11, for synthetic gums and resins not specially provided for, 4 cents per pound and 30 percent ad valorem on foreign value.
Broadening use of synthetic resins.
The application of synthetic resins has extended into practically every branch of industry. This marked expansion is not surprising when the adaptability of these products is considered. Their uses range from jewelry and bottle closures to building materials; from adhesives and new types of surface coatings to light reflectors and shades. They are being substituted for natural materials, such as wood, metal, and glass at an increasing rate. They have provided new uses for raw materials formerly used in antiseptics, disinfectants, explosives, embalming fluids, fertilizers, moth repellants, and as solvents. The speed of expansion of their use in resin manufacture has been such as to create a serious shortage of some of these raw materials.
New applications for synthetic resins appear almost daily They are used in furniture, wall panels, builders’ hardware, electrical fixtures, and in thousands of small appliances. The automobile industry is probably the largest single user. An interesting application here is in silent gears and shaft bearings where the use of synthetic resins makes water lubrication possible. Other automotive uses are in distributor heads, horn buttons, gear shift knobs, dome light reflectors, control knobs and the finishing lacquers. Additional uses contemplated for the near future are in accelerator pedals and instrument panels. A new type of safety glass in which vinyl resins are used was introduced in 1936.
In decorative uses remarkable progress has been made. Panels of laminated resins are widely used in store fronts, lobbies of office buildings,
and hotels; doors faced with this material are in use. The liner Queen Mary is paneled, in part, with laminated resins, as is the annex to the Library of Congress. Lamp shades of urea resin are used in many Pullman cars and are available for home and office use.
Other things being equal, the cheaper a synthetic resin, the more widely it may be applied as a substitute for other materials. As a result many an apparently useless byproduct, such as oat hulls which yield furfural, is either already used or being tested as a source of raw material. Other materials which have already found a place or may do so, are soybean meal, sugar, and certain petroleum distillates.
Each of the important groups of synthetic resins has been sponsored by one or more manufacturers of established reputation and large capital resources. When a product reaches the commercial stage, after heavy research cost, its future importance is therefore usually assured.
Relation of synthetic resins to their raw materials.
Most of the commercially important synthetic resins are derived directly or indirectly from coal. The chart (p. 6) shows the derivation of certain synthetic resins from the principal raw materials used in their manufacture and the intermediate products back to the original source of the material.
The polystyrene resins, for example, are made by polymerizing styrene or vinyl benzene. Although basically from ethylene and benzene, vinyl benzene may be formed in several ways. Ethylene is found in the gases from the destructive distillation of coal but is obtained commercially by cracking natural gas or petroleum. Styrene, found already formed in the light oil fractions from coal tar, causes gum-forming in motor benzol and certain industrial gases.
When coke and lime are mixed and heated in an electric furnace to 2,000° C., calcium carbide is formed. This compound with water yields acetylene, the starting point for a long list of important products, including several types of synthetic resins. When acetylene gas is passed through acetic acid (itself obtained from acetylene) vinyl acetate is obtained. If hydrochloric acid is used instead of acetic acid, vinyl chloride is obtained. These compounds, when polymerized, yield the vinyl resins. The acrylate resins may be obtained from the same basic raw material by an entirely different procedure. Synthetic rubber is also derived from acetylene, as are acetic anhydride and acetic acid (used in making cellulose acetate plastics) and many other chemicals of commercial importance.
Derivation of certain synthetic resins
When naphthalene (from coal tar) is treated with air at elevated temperatures, phthalic anhydride is formed. Substituting benzene for naphthalene yields maleic anhydride. Both of these substances when condensed with glycerin, a byproduct of the soap industry, yield alkyd resins.
The tar acids from coal tar, either separated or mixed, when condensed with formaldehyde give the highly important tar-acid resins. Or if formaldehyde is condensed with urea, obtained from carbon dioxide and ammonia, the urea resins are formed.
The chart indicates the synthetic resins which are thermoplastic, that is, which become plastic again upon reheating, and those which are thermosetting, that is, pass into an infusible stage at a certain critical temperature and pressure and do not again become plastic upon subsequent reheating.
Sources of information.
The data used in this report were obtained from a great variety of sources. The several American and British trade journals were freely consulted as were the various text books on this subject. Much of the information on the domestic industry was obtained by personal contact with producers and by correspondence. Field work included visits to most of the domestic producers
of resins and a representative group of fabricators. Information of this type which was nonconfidential or which could be combined so as not to reveal individual operations was invaluable. Even where it was such that it could not be published it became part of the general background.
The data pertaining to the industry in foreign countries were, for the most part, furnished the Tariff Commission by Department of Commerce representatives stationed abroad, in response to inquiries by the Commission.
2. SUMMARY
Growth of the industry.
The coal-tar synthetic resin industry in the United States began on a small scale some years before the World War. The output then was confined to a few types of tar-acid resins and the applications were quite limited until 1927, when certain of the basic patents expired. The output of about 1.5 million pounds in 1921 had increased to more than 13 million pounds in 1927 and the average unit value of sales had dropped from 81 cents per pound to 47 cents. Production continued to increase and the unit value to decrease annually until 1932 when general economic conditions forced a slight curtailment for 1 year. Since then the annual increase in volume and variety has been rapid. Production of non-coal-tar synthetic resins was started on a small scale in 1929 when both urea and vinyl resins entered the picture. Commercial production of the petroleum resins began in 1936 and of the acrylate resins in 1937. Table 1 shows the production and sales of coal-tar resins and of non-coal-tar resins, from 1921 through 1937.
T 1. Synthetic resins: United States production and sales, 1921-37
1 Does not include resins from adipic acid, coumarone and indene, hydrocarbon, polystyrene, succinic acid and sulfonamides With the exception of coumarone and indene resins in recent years production of the resins not included was small
2 Not publishable Figures would reveal operations of individual producers
Source: Compiled from annual reports of the Tariff Commission on dyes and other synthetic organic chemicals in the United States.
Many factors have contributed to the growth of the synthetic resin industry. Among these are the intensive research and development work carried on by many individuals and firms; their widespread application in many fields competing with wood, metal, and glass; and the development of processes for raw materials which have greatly reduced their cost and made their wider use possible.
Raw materials.—Although the chief raw materials consumed in the synthetic resin industry are coal-tar derivatives and formaldehyde, many others are utilized. The rapid expansion of the industry has created new demands for materials in increasing quantities and has not only increased the markets for well-known materials but has resulted in the production on a huge scale of materials entirely new to commerce. Practically all the raw materials now used can be derived from a few natural substances, such as air, water, coal, petroleum crudes, salt, sulphur, and limestone. The air yields nitrogen which may be converted to ammonia, a raw material for urea, one of the components of the urea resins. Coal, as is well known, yields a great variety of substances, many of which are essential to synthetic resin manufacture. Benzene is the starting point for synthetic phenol; naphthalene is used to make phthalic anhydride and maleic anhydride; coke is converted to calcium carbide, which in turn yields acetylene, acetic acid, and many other synthetics; carbon monoxide which is converted to methanol and formaldehyde; and the natural tar acids such as phenol, the cresols, and the xylenols. Limestone is a component of calcium carbide, and salt yields needed alkalies and acids. Water is broken down, and the hydrogen is converted to ammonia, methanol, formaldehyde, and ethylene.
Some idea of the expansion in production of these raw materials whose principal use is in synthetic resins may be had by comparing the output in 1923 of tar acids, formaldehyde, phthalic anhydride, maleic anhydride, urea, vinyl acetate, and vinyl chloride, which amounted to 35 million pounds, with the output of 270 million pounds in 1936. The manufacture of these materials is largely by coal-tar distilling companies and makers of chemicals.
Resins.—The coal-tar resins are the most important in quantity, value, and variety of application. This class includes four groups: (a) tar acid, (b) alkyd, (c) coumarone and indene, and (d) polystyrene. Of these, resins from tar acids (phenol, cresols, and xylenols) are produced in the largest quantity, the output having increased from about 15 million pounds in 1932 to about 80 million pounds in 1937. In the latter year about 40 percent of the consumption of tar acid
resins was in molded articles, 25 percent in paint and varnishes, 20 percent in laminated products, and 15 percent in miscellaneous uses.
The alkyd resins have shown a remarkable increase in output. Production totaled slightly less than 10 million pounds in 1933; in 1937 it amounted to about 61 million pounds. Practically all of the alkyds have been consumed in paints and varnishes.
The coumarone and indene resins have increased steadily over a number of years and are now one of the most important groups.
The polystyrene resins have been in an experimental stage for a long time, with the volume of production small. In 1937, however, commercial production of a water-white product was announced, and it is believed that the output of these resins will increase sharply in the near future.
The non-coal-tar resins were of little importance prior to 1930 and production amounted to less than 2 million pounds in 1932. Since then, however, progress has been rapid, both in types and output. Resins from urea constitute an important part of this class and the output has increased practically every year since 1929 when production was started. Most of the output is used in molded articles where light and pastel shades are required. In 1936, for the first time, appreciable quantities were consumed in laminating and in surface coatings.
The vinyl resins have been produced in increasing quantities for the past 8 years. Production reached a new high in 1937, and with the acceptance of this type of resin for safety glass laminations it is expected that the output will increase materially in the near future. In 1937 the application in surface coatings, molded articles, and laminations were of approximately equal importance.
The acrylate resins are among the newest commercial developments in this industry. Of the several types now manufactured, one appears valuable in surface coatings and adhesives and another, in the form of its cast or molded polymer, in airplane windows, machined articles, and lenses.
Petroleum resins were first produced in commercial quantities in 1936, but the output in that year was appreciable. These low-priced synthetics are used in surface coatings, laminations, and miscellaneous uses.
The industry abroad.
World production of synthetic resins at this time is estimated at 300 million pounds annually, of which the United States accounts for 45 percent. Germany produces about 27 percent and Great Britain about 20 percent of the total and a number of countries including France, Italy, Czechoslovakia, Canada, and Japan produce the remainder. Practically all types are made in Germany and Great Britain although in lesser quantities than here. The urea resins originated abroad, as did the acrylates and polystyrenes.
Commercial development of the synthetic resins abroad has been somewhat behind that in the United States, although in recent years the increase there has been so rapid as to seriously affect the international raw material market. Germany, formerly one of our principal sources of crude naphthalene, for a time restricted exports of that commodity in order to conserve the available supply for home consumption, presumably in alkyd resins. Great Britain, formerly the principal exporter of phenol, has found it necessary to supplement production of natural phenol with synthetic phenol. It is possible that in the future similar conditions may arise in world markets for cresylic acid.
International trade.
International trade in the synthetic resins has been small. Germany has been the principal exporting country. There are a number of reasons for the negligible movement of these materials in international trade, the chief of which are active home markets in the principal producing countries; the existence of patents of a basic nature which limited trade to the owners and licencees under them;
