Mathematics – Probability
Scientific paper
2008-11-12
Annals of Applied Probability 2008, Vol. 18, No. 5, 1737-1770
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/07-AAP503 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/07-AAP503
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].
Dolinsky Yan
Kifer Yuri
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