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Pricing American Options in a Mild Stochastic Environment

7 Pages Posted: 6 Mar 2008 Last revised: 16 Jun 2008

Moisa Altar

Bucharest Academy of Economic Studies

Judita Samuel

Bucharest Academy of Economic Studies

Date Written: June 2008

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

JEL Classification: C61, D99, E31, E41, E62, E63, H62, H63, O4

Suggested Citation

Altar, Moisa and Samuel, Judita, Pricing American Options in a Mild Stochastic Environment (June 2008). Available at SSRN: https://ssrn.com/abstract=1102582 or http://dx.doi.org/10.2139/ssrn.1102582

Moisa Altar (Contact Author)

Bucharest Academy of Economic Studies ( email )

6, Romana Square, District 1
Bucharest, 010374
Romania

HOME PAGE: http://www.dofin.ase.ro

Judita Samuel

Bucharest Academy of Economic Studies ( email )

6, Romana Square, District 1
Bucharest, 010374
Romania

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