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Efficient Computation of Hedging Portfolios for Options with Discontinuous Payoffs

Cvitanić, Jakša and Ma, Jin and Zhang, Jianfeng (2003) Efficient Computation of Hedging Portfolios for Options with Discontinuous Payoffs. Mathematical Finance, 13 (1). pp. 135-151. ISSN 0960-1627. http://resolver.caltech.edu/CaltechAUTHORS:20111007-134050070

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Abstract

We consider the problem of computing hedging portfolios for options that may have discontinuous payoffs, in the framework of diffusion models in which the number of factors may be larger than the number of Brownian motions driving the model. Extending the work of Fournié et al. (1999), as well as Ma and Zhang (2000), using integration by parts of Malliavin calculus, we find two representations of the hedging portfolio in terms of expected values of random variables that do not involve differentiating the payoff function. Once this has been accomplished, the hedging portfolio can be computed by simple Monte Carlo. We find the theoretical bound for the error of the two methods. We also perform numerical experiments in order to compare these methods to two existing methods, and find that no method is clearly superior to others.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1111/1467-9965.00010 DOIUNSPECIFIED
http://onlinelibrary.wiley.com/doi/10.1111/1467-9965.00010/abstractPublisherUNSPECIFIED
Additional Information:© 2003 Blackwell Publishing Inc. Article first published online: 7 Mar. 2003. The authors thank P. Glasserman for useful comments. The first author’s research was supported in part by NSF grant DMS-00-99549. Work by the second and third authors was supported in part by NSF grant 9971720.
Funders:
Funding AgencyGrant Number
NSFDMS-00-99549
NSF9971720
Subject Keywords:hedging options; malliavin calculus; Monte Carlo methods
Record Number:CaltechAUTHORS:20111007-134050070
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111007-134050070
Official Citation:Cvitanić, J., Ma, J. and Zhang, J. (2003), Efficient Computation of Hedging Portfolios for Options with Discontinuous Payoffs. Mathematical Finance, 13: 135–151. doi: 10.1111/1467-9965.00010
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27128
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Oct 2011 20:25
Last Modified:26 Dec 2012 14:15

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