APPROXIMATE OPTION VALUATION FOR ARBITRARY STOCHASTIC PROCESSES

Robert Jarrow () and Andrew Rudd
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Andrew Rudd: Cornell University, Ithaca, NY 14853, USA

Chapter 1 in Financial Derivatives Pricing:Selected Works of Robert Jarrow, 2008, pp 9-31 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe show how a given probability distribution can be approximated by an arbitrary distribution in terms of a series expansion involving second and higher moments. This theoretical development is specialized to the problem of option valuation where the underlying security distribution, if not lognormal, can be approximated by a lognormally distributed random variable. The resulting option price is expressed as the sum of a Black–Scholes price plus adjustment terms which depend on the second and higher moments of the underlying security stochastic process. This approach permits the impact on the option price of skewness and kurtosis of the underlying stock's distribution to be evaluated.

Keywords: Derivatives; Options; Hedging; HJM; Black–Scholes; Forwards; Futures; Martingale Measure; Calls; Puts; Market Manipulation; Margin Requirements (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Approximate option valuation for arbitrary stochastic processes (1982)
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