PRICING OPTIONS ON RISKY ASSETS IN A STOCHASTIC INTEREST RATE ECONOMY

Kaushik I. Amin and Robert Jarrow ()
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Kaushik I. Amin: School of Business Administration, University of Michigan, Ann Arbor, MI, USA

Chapter 15 in Financial Derivatives Pricing:Selected Works of Robert Jarrow, 2008, pp 327-347 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThis paper studies contingent claim valuation of risky assets in a stochastic interest rate economy. The model employed generalizes the approach utilized by Heath, larrow, and Morton (1992) by imbedding their stochastic interest rate economy into one containing an arbitrary number of additional risky assets. We derive closed form formulae for certain types of European options in this context, notably call and put options on risky assets, forward contracts, and futures contracts. We also value American contingent claims whose payoffs are permitted to be general functions of both the term structure and asset prices generalizing Bensoussan (1984) and Karatzas (1988) in this regard Here, we provide an example where an American call's value is well defined, yet there does not exist an optimal trading strategy which attains this value. Furthermore, this example is not pathological as it is a generalization of Roll's (1977) formula for a call option on a stock that pays discrete dividends.

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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