博弈期权短缺风险的二项式近似
Binomial approximations of shortfall risk for game options
摘要：
我们发现，在离散和连续时间的情况下，考虑Lipschitz连续路径依赖的回报，二项式近似的博弈（以色列）期权的短缺风险收敛到相应的Black-Scholes市场的短缺风险。这些结果对于通常的美式选择也是新的。本文继续并扩展了Kifer [Ann. Appl. Probab. 16（2006）984--1033]，其中获得了对游戏期权价格的二项式近似值的估计。我们的论点，特别是依赖于强不变原理型近似通过Skorokhod嵌入，估计Kifer [安。16（2006）984--1033]和Dolinsky和Kifer [Stochastics 79（2007）169--195]建立的离散时间中最优短缺套期保值的存在性。
英文摘要：
We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black--Scholes market considering Lipschitz continuous path-dependent payoffs for both discrete- and continuous-time cases. These results are new also for usual American style options. The paper continues and extends the study of Kifer [Ann. Appl. Probab. 16 (2006) 984--1033] where estimates for binomial approximations of prices of game options were obtained. Our arguments rely, in particular, on strong invariance principle type approximations via the Skorokhod embedding, estimates from Kifer [Ann. Appl. Probab. 16 (2006) 984--1033] and the existence of optimal shortfall hedging in the discrete time established by Dolinsky and Kifer [Stochastics 79 (2007) 169--195].
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