The Valuation of Compound Options and American Calls on Dividend Paying Stocks with Time-Varying Volatility
THE J. OF FINANCIAL ENGINEERING, Vol. 5 No. 3, September 1996
Posted: 21 Nov 1996
Abstract
This paper extends Geske's (1979a) compound European call option pricing model and the Roll (1977), Geske (1979b), and Whaley (1981) (RGW) American call pricing model to the case where the variance of the underlying asset changes deterministically. The theoretical analysis shows that the generalized models use integrals of the time-varying variance in the same way as Merton's (1973) generalization of the Black and Scholes (1973) European option pricing model. The resulting analytic expressions require two variance parameters and an adjusted correlation coefficient for the relevant bivariate normal distribution. The comparison of our time-varying model with RGW reveals small differences which may vary in sign. For at-the-money options, if stock variability decreases after dividend payment dates, then initial RGW prices are biased low; conversely, RGW prices are too high if variability has a tendency to increase after dividends.
JEL Classification: G12, G13
Suggested Citation: Suggested Citation