Error estimates for binomial approximations of game options

• 成果类型: Article
• 署名作者: Kifer, Yuri
• 署名单位: Hebrew University of Jerusalem
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000088
• 发表日期: 2006
• 页码: 984-1033
• 关键词: convergence; american

摘要

We justify and give error estimates for binomial approximations of game (Israeli) options in the Black-Scholes market with Lipschitz continuous path dependent payoffs which are new also for usual American style options. We show also that rational (optimal) exercise times and hedging self-financing portfolios of binomial approximations yield for game options in the Black-Scholes market nearly rational exercise times and nearly hedging self-financing portfolios with small average shortfalls and initial capitals close to fair prices of the options. The estimates rely on strong invariance principle type approximations via the Skorokhod embedding.