Pricing American Options in a Mild Stochastic Environment
AbstractThe problem of pricing derivative financial products is central to the theory of capital markets. An option is a financial contract conveying its owner the right of buying or selling a financial asset (underlying asset) at a preset strike price K, at a fixed expiration date T (maturity). Unlike European options, which can be exercised only at maturity date, an American option can be exercised at any time t prior to the maturity date. Most of the option pricing methods, starting with the well-known Black-Scholes model (1973), are based on the assumption that the market uncertainty can be modeled by a Wiener process. In this context, while it is possible to obtain convenient analytical option pricing formulae for European options, it is very difficult to obtain exact results for American options. In the present paper, we assume that the market uncertainty is modeled by a more regular stochastic process, which was called, by A. Halanay, a mild stochastic environment. In this context, we are able to obtain precise stopping rules, determining the exact exercise time and the exact price of an American option.
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Bibliographic InfoPaper provided by Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB in its series Advances in Economic and Financial Research - DOFIN Working Paper Series with number 11.
Date of creation: Jun 2008
Date of revision:
american option; option pricing; mild stochastic environment;
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- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
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- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
- Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 5(2), pages 251-258, November.
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