A Concept of News Impact Curve and Asymmetry in Modelling Capital Markets
The importance of volatility modeling is clear from the wide scope of applications ranging from forecasting stock returns, through options pricing to risk valuation.
redictability of financial instruments volatility is one of the key aspects in the area of financial market research. The importance of volatility modeling is clear from the wide scope of applications ranging from forecasting stock returns, through options pricing to risk valuation. The variety of volatility models proposed in financial literature created a need for a convenient tool that would allow one to analyze their properties. One method that comes in handy whenever there is need to compare volatility models is the concept of a NEWS IMPACT CURVE. The family of ARCH models reflects one of the most popular approaches to volatility modeling. The underlying concept is to develop a model for volatility, based on its past values, instead of assuming a variance (which is a measure for volatility) constant in time. The idea is supported by the observation of the so called volatility clustering phenomenon i.e. a tendency for low volatility levels to be followed by consequent low volatilities and for high volatility – to imply other rapid fluctuations. A clear economic interpretation of volatility clustering is that investors who find themselves in times of sharp upswings and drops in prices seek to realize profits or avoid further losses by buying or selling instruments. In the basic ARCH model for a stock return (Engle, 1982, see table 1) the conditional variance is modelled on lagged values of ’s, meaning that past shocks decide on current volatility ( is used to denote deviation of the realization of a stock return from its expected value; see table 1). Squared values
models give exactly the same shape of the of are taken, giving the effect that only the news impact curve (depicted in figure 1). size of a past disturbance has its influence A rise in absolute value of past disturbance on volatility, not the sign. A generalization in the form of a GARCH model (Bollerslev, 1986, Conditional mean equation: see table 1) adds lagged yt E ( yt | Ft 1 ) t where t ~ N (0, ht ), yt denotes the explained values of variance to the above model, solving the stock return and Ft is a set of relevant information available at time t problem of overparameConditional variance equation in: trization. To analyze the effect that • ARCH(1): past news has on current ht t21 , volatility in different • GARCH(1,1): models of an ARCH family, the concept of ht t21 ht 1 , a news impact curve co• Nonlinear ARCH(1,1): mes in handy. The news ht | t 1 | ht 1 , impact curve is a function relating volatility • Multiplicative ARCH(1): at time to a shock caulog(ht ) log( t21 ) , sed by news arrival at time (measured by • Exponential GARCH(1,1): ). The curve is con | | 2, log(ht ) log(ht 1 ) t 1 t 1 structed holding con h ht 1 t 1 stant information dated and earlier with • GJR GARCH(1,1): all lagged values of con ht ht 1 t21 St1 t21 where St 1 ditional variance at the if t 0 and St 0 otherwise, level of unconditional variance of stock return. • Asymmetric GARCH(1,1): Based on the relation ht ( t 1 ) 2 ht 1 , between current volatility and news lagged only • VGARCH(1,1): one period, the news 2 impact curve does not t 1 ht 1 , ht focus on further dyna h mic properties of mo t 1 dels. That is the reason where , , , are constant parameters. why ARCH and GARCH
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