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Optimal hedging of American options in discrete time. (English) Zbl 1247.91201

Carmona, René A. (ed.) et al., Numerical methods in finance. Selected papers based on the presentations at the workshop, Bordeaux, France, June 2010. Berlin: Springer (ISBN 978-3-642-25745-2/hbk; 978-3-642-25746-9/ebook). Springer Proceedings in Mathematics 12, 145-170 (2012).
Summary: In this article we study the price of an American style option based on hedging the underlying assets in discrete time. Like its European style analog, the value of the option is not given in general by an expectation with respect to an equivalent martingale measure. We provide the optimal solution that minimizes the hedging error variance. When the assets dynamics are Markovian or a component of a Markov process, the solution can be approximated easily by numerical methods already proposed for pricing American options. We proceed to a Monte Carlo experiment in which the hedging performance of the solution is evaluated. For assets returns that are either Gaussian or Variance Gamma, it is shown that the proposed solution results in lower root mean square hedging error than with traditional delta hedging.
For the entire collection see [Zbl 1238.91005].

MSC:

91G60 Numerical methods (including Monte Carlo methods)
91G20 Derivative securities (option pricing, hedging, etc.)
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