On the Pricing of American Options.
Technical rept. Sep 85-Aug 86,
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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In an important and relatively recent article Bensoussan presents a rigorous treatment of the pricing problem for contingent claims that can be exercised at any time before maturity. He adapts to this situation the Black Scholes methodology of duplicating the cash flow from such a claim by managing skillfully a self-financing portfolio that contains only the basic instruments of the market, i.e., the stocks and the bond, and that entails no arbitrage opportunities before exercise. Under a condition on the market model called completeness Bensoussan shows that the valuation of such claims is indeed possible and characterizes the exercise time in terms of an appropriate optimal stopping problem. In the study of the latter, Bensoussan employs the so-called penalization method, which forces rather stringent boundedness and regularity conditions on the payoff from the contingent claim. Such conditions are not satisfied, however, by the prototypical examples of such claims, i.e., American call options. The aim of this paper is to offer an alternative methodology on this problem, which is actually simpler and manages to remove the above restrictions.
- Economics and Cost Analysis
- Theoretical Mathematics