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].
Publié le : 2008-10-15
Classification:
Game options,
Dynkin games,
complete and incomplete markets,
shortfall risk,
binomial approximation,
Skorokhod embedding,
91B28,
60F15,
91A05
@article{1225372948,
author = {Dolinsky, Yan and Kifer, Yuri},
title = {Binomial approximations of shortfall risk for game options},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 1737-1770},
language = {en},
url = {http://dml.mathdoc.fr/item/1225372948}
}
Dolinsky, Yan; Kifer, Yuri. Binomial approximations of shortfall risk for game options. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 1737-1770. http://gdmltest.u-ga.fr/item/1225372948/