Weighted Monte Carlo: Calibrating the Smile and Preserving Martingale Condition
AbstractWeighted Monte Carlo prices exotic options calibrating the probabilities of previously generated paths by a regular Monte Carlo to fit a set of option premiums. When only vanilla call and put options and forward prices are considered, the Martingale condition might not be preserved. This paper shows that this is indeed the case and overcomes the problem by adding additional synthetic options. A robust, fast and easy-to-implement calibration algorithm is presented. The results are illustrated with a geometric cliquet option which shows how the price impact can be significant.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1102.3541.
Date of creation: Feb 2011
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Publication status: Published in Risk Magazine, Vol. 19, No. 5, May 2006
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Web page: http://arxiv.org/
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