Translator Disclaimer
October 2008 Binomial approximations of shortfall risk for game options
Yan Dolinsky, Yuri Kifer
Ann. Appl. Probab. 18(5): 1737-1770 (October 2008). DOI: 10.1214/07-AAP503

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].

Citation

Download Citation

Yan Dolinsky. Yuri Kifer. "Binomial approximations of shortfall risk for game options." Ann. Appl. Probab. 18 (5) 1737 - 1770, October 2008. https://doi.org/10.1214/07-AAP503

Information

Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1151.91504
MathSciNet: MR2462547
Digital Object Identifier: 10.1214/07-AAP503

Subjects:
Primary: 91B28
Secondary: 60F15, 91A05

Rights: Copyright © 2008 Institute of Mathematical Statistics

JOURNAL ARTICLE
34 PAGES


SHARE
Vol.18 • No. 5 • October 2008
Back to Top