Pricing American Options in a Mild Stochastic Environment
Moisa Altar and
Judita Samuel
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Judita Samuel: Bucharest University of Economics
No 11, Advances in Economic and Financial Research - DOFIN Working Paper Series from Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB
Abstract:
The 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.
Keywords: american option; option pricing; mild stochastic environment (search for similar items in EconPapers)
JEL-codes: C61 D99 E31 E41 E62 E63 H62 H63 O4 (search for similar items in EconPapers)
Date: 2008-06
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