Abstract
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].
Original language | English |
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Pages (from-to) | 1737-1770 |
Number of pages | 34 |
Journal | Annals of Applied Probability |
Volume | 18 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2008 |
Keywords
- Binomial approximation
- Complete and incomplete markets
- Dynkin games
- Game options
- Short-fall risk
- Skorokhod embedding