Binomial approximations of shortfall risk for game options

Yan Dolinsky*, Yuri Kifer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 languageAmerican English
Pages (from-to)1737-1770
Number of pages34
JournalAnnals of Applied Probability
Volume18
Issue number5
DOIs
StatePublished - Oct 2008

Keywords

  • Binomial approximation
  • Complete and incomplete markets
  • Dynkin games
  • Game options
  • Short-fall risk
  • Skorokhod embedding

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