Approximation of American put prices by European prices via an embedding method

• 成果类型: Article
• 署名作者: Jourdain, B; Martini, C
• 署名单位: Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 196-223
• 关键词: free-boundary; OPTION

摘要

In mathematical finance, the price of the so-called American Put option is given by the value function of the optimal-stopping problem with the option payoff psi: x --> (K - x)(+) as a reward function. Even in the Black-Scholes model, no closed-formula is known and numerous numerical approximation methods have been specifically designed for this problem. In this paper, as an application of the theoretical result of B. Jourdain and C. Martini [Ann. Inst. Henri Paincare Anal. Nonlinear 18 (2001) 1-17], we explore a new approximation scheme: we look for payoffs as close as possible to psi, the American price of which is given by the European price of another claim. We exhibit a family of payoffs <(phi)over cap(h)> indexed by a measure h, which are continuous, match with (K - x)(+) outside of the range ]K*, K[ (where K* is the perpetual Put strike), are analytic inside with the right derivative (-1) at both ends. Moreover a numerical procedure to select the best h in some sense yields nice results.