"Interest Theory:
Financial Mathematics and Deterministic Asset Valuation"
(2nd Edition) provides a foundational approach to financial mathematics, particularly focusing on deterministic models for asset valuation. Authored for students, actuaries, and finance professionals, this book covers core topics in interest theory, valuation of cash flows, and bonds, as well as practical applications like amortization schedules and annuity payments.
Part 1: Fundamentals of Interest Theory
Chapter 1: Basic Concepts of Interest Rates
The book starts with the fundamental concept of interest rates, explaining simple versus compound interest and their applications. Simple interest applies to short-term investments, whereas compound interest, which compounds on previously earned interest, is central to long-term financial calculations. The authors describe different
compounding periods, including annual, semiannual, and quarterly compounding, demonstrating how compounding frequency influences the accumulated value.
Chapter 2: Time Value of Money
One of the most critical ideas in finance, the time value of money (TVM), asserts that money today is worth more than money in the future due to its earning potential. This chapter introduces present and future value calculations, showing how to discount future cash flows to assess their current worth. It discusses various formulas for computing present and future values, using examples to highlight practical applications in loan repayments, investments, and savings.
Chapter 3: Effective and Nominal Interest Rates
Interest rates are often quoted on different bases, and this chapter explains how to convert between nominal and effective rates. The nominal rate refers to the stated rate, while the effective rate takes compounding into account. The authors provide formulas to convert nominal rates with varying
compounding periods into effective rates, a concept essential for comparing different investment and loan options on an equal basis.
Chapter 4: Force of Interest
The force of interest is a continuous compounding concept useful in actuarial science and financial modeling. It describes how an interest rate changes over an infinitesimally small period. The chapter provides a mathematical framework for continuous compounding, showing how to apply the force of interest in various financial scenarios, such as valuing perpetuities and annuities.
Part 2: Annuities and Cash Flows
Chapter 5: Annuities and Perpetuities
An annuity is a series of periodic payments, while a perpetuity is an annuity with no end. This chapter delves into different types of annuities—immediate, deferred, ordinary, and due. The authors provide formulas for calculating present and future values of each type. Additionally, the chapter explains how perpetuities, such as preferred stocks, are valued,
emphasizing the importance of these instruments in both finance and actuarial studies.
Chapter 6: Cash Flow Valuation
The value of a financial asset is determined by its future cash flows. Here, the authors present methods for valuing cash flows, considering factors like payment timing, frequency, and amount. This chapter covers general cash flow streams, discounted cash flow (DCF) analysis, and the concept of net present value (NPV) for decisionmaking. The emphasis is on applying these methods in evaluating investments, bonds, and annuities.
Chapter 7: Sinking Funds and Loan Amortization
Sinking funds and amortization are practical applications of interest theory. A sinking fund is an account set aside to repay a debt or bond, while amortization spreads a loan payment over a set term. The authors provide formulas to determine sinking fund payments and develop amortization schedules. Examples demonstrate these concepts in personal finance, such as mortgage repayments, car loans, and business debt repayment strategies.
Part 3: Deterministic Asset Valuation
Chapter 8: Deterministic Valuation of Bonds
Bonds are a key application of deterministic asset valuation, and this chapter explores how bond prices are affected by interest rates and cash flows. It introduces the fundamental bond valuation formula and discusses important bond characteristics like par value, coupon rate, and maturity date. Concepts like yield to maturity (YTM), current yield, and bond duration are also covered, providing readers with a thorough understanding of bond investment analysis.
Chapter 9: Term Structure of Interest Rates
The term structure of interest rates, or yield curve, shows the relationship between interest rates and time to maturity for bonds of similar credit quality. This chapter explains the theories behind the term structure, including expectations theory, liquidity preference theory, and market segmentation theory. It demonstrates how to interpret yield curves and use them to make investment decisions or predict economic conditions.
Chapter 10: Bond Immunization and Duration
Duration is a measure of a bond’s sensitivity to interest rate changes, crucial for managing interest rate risk. The chapter explains how duration helps investors and portfolio managers immunize portfolios against interest rate fluctuations. Modified duration and convexity are also introduced, offering more precise tools for assessing bond price sensitivity. Bond immunization strategies are discussed, including matching asset and liability durations to safeguard against adverse interest rate movements.
Part 4: Advanced Financial Mathematics Applications
Chapter 11: Amortization of Loans and Debts
This chapter provides an in-depth look at loan amortization, showing various methods for repaying debt over time. It introduces amortization schedules and details different repayment structures, such as fixed principal payments and fixed installment payments. Formulas for calculating outstanding loan balances, principal repayments, and interest expenses are presented, with examples relevant to mortgages, business loans, and credit card debt.
Chapter 12: Interest Rate Risk and Sensitivity Analysis
Interest rate risk is a fundamental concern for both investors and institutions. Here, the authors present tools for measuring and managing interest rate risk, such as sensitivity analysis and scenario testing. The chapter covers various techniques for stresstesting portfolios and evaluating how changes in interest rates impact asset values. It’s particularly relevant for banks, insurance companies, and pension funds that are exposed to long-term interest rate fluctuations.
Chapter 13: Valuing Derivative Securities with Deterministic Interest Rates
Derivatives, such as options and futures, derive their value from underlying assets. This chapter explains how to value derivative securities in a deterministic interest rate environment. Concepts like forward contracts, futures, and swaps are introduced, with formulas for calculating their value. The authors provide examples of how derivatives can be used for hedging, speculation, or arbitrage, emphasizing the importance of these instruments in managing risk.
Part 5: Practical Applications and Case Studies
Chapter 14: Application to Personal Financial Planning
This chapter applies interest theory to personal financial planning, covering retirement savings, education funding, and life insurance. It explains how to use annuities, sinking funds, and investment strategies to achieve long-term financial goals. The authors emphasize the importance of time value of money calculations and effective interest rates in personal finance decisions.
Chapter 15: Application to Corporate Finance and Capital Budgeting
Corporate finance applications of interest theory include capital budgeting and project evaluation. This chapter presents techniques like net present value (NPV) and internal rate of return (IRR) for evaluating corporate projects. Examples illustrate how firms use these methods to assess potential investments, considering both timing and risk of cash flows. Concepts such as hurdle rates and capital costs are also discussed.
Chapter 16: The Role of Financial Mathematics in Actuarial
Science
Interest theory has a significant role in actuarial science, particularly in valuing insurance liabilities and pension funds. This chapter explores actuarial applications, such as premium calculation, reserve valuation, and annuity pricing. It introduces actuarial notation and methodologies, linking interest theory with life contingencies and mortality tables to estimate insurance policy values accurately.
Appendices: Mathematical and Financial Formulas
The book concludes with appendices containing essential mathematical and financial formulas, from basic algebraic operations to advanced calculus. These appendices provide a quick reference for formulas, such as those used for annuities, present values, and derivatives.
The 2nd Edition of "Interest Theory: Financial Mathematics and Deterministic Asset Valuation" by S. David Promislow serves as a comprehensive resource on deterministic asset valuation, blending foundational financial mathematics with practical applications. By covering fundamental interest
concepts, deterministic asset valuation, and advanced financial applications, this book provides a strong mathematical framework for anyone pursuing a career in finance, actuarial science, or personal financial planning. Find the Full Original Textbook (PDF) in the link