Shortfall Risk Approximations for American Options in the Multidimensional Black-Scholes Model

We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black-Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path-dependent payoffs. In comparison to previou...

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Bibliographic Details
Published in:Journal of applied probability 2010-12, Vol.47 (4), p.997-1012
Main Author: Dolinsky, Yan
Format: Article
Language:English
Subjects:
60F05
91B28
Algorithms
American option
Applications
Approximation
Budget deficits
Comparative analysis
Convergence
Exact sciences and technology
Investment risk
Markets
Martingales
Mathematics
Options markets
Probabilities
Probability and statistics
Random variables
Risk
Sciences and techniques of general use
Self financing portfolio
shortfall risk
Statistics
Stochastic models
Stochastic processes
Studies
weak convergence
Citations: Items that this one cites
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Description
Summary:We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black-Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path-dependent payoffs. In comparison to previous papers we consider the multiassets case for which we use the weak convergence approach.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1294170514