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

See all articles by Steven B. Raymar

Steven B. Raymar

Fordham University - Finance Area

Aamir M. Sheikh

Barra, Inc.

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

Raymar, Steven B. and Sheikh, Aamir M., 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, Available at SSRN: https://ssrn.com/abstract=7927

Steven B. Raymar (Contact Author)

Fordham University - Finance Area ( email )

33 West 60th Street
New York, NY 10023
United States
212-636-6159 (Phone)
212-765-5573 (Fax)

Aamir M. Sheikh

Barra, Inc.

88 Pine Street
2nd Floor
New York, NY 10005
United States

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