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Weighted Monte Carlo: Calibrating the Smile and Preserving Martingale Condition

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  • Alberto Elices
  • Eduard Gim'enez

Abstract

Weighted 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.

Suggested Citation

  • Alberto Elices & Eduard Gim'enez, 2011. "Weighted Monte Carlo: Calibrating the Smile and Preserving Martingale Condition," Papers 1102.3541, arXiv.org.
    • Handle: RePEc:arx:papers:1102.3541
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    References listed on IDEAS

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    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. S'andor Kuns'agi-M'at'e & G'abor F'ath & Istv'an Csabai & G'abor Moln'ar-S'aska, 2022. "Deep Weighted Monte Carlo: A hybrid option pricing framework using neural networks," Papers 2208.14038, arXiv.org, revised Dec 2022.

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