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Option pricing and hedging with minimum local expected shortfall

Author

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  • Benoit Pochart
  • Jean-Philippe Bouchaud

Abstract

We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk critcrion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the presence of transaction costs. We illustrate the method on plain vanilla options when the price returns follow a Student -t distribution. We show that in the presence of fat-tails, our strategy allows us to significantly reduce extreme risks, and generically loads to low Gamma hedging. He also find that using an asymmetric risk function generates option skews, even when the underlying dynamics is unskewed. Finally, we show the proper accounting of transaction costs leads to an optimal strategy with reduced Gamma, which is found to outperform Leland's hedge.

Suggested Citation

  • Benoit Pochart & Jean-Philippe Bouchaud, 2004. "Option pricing and hedging with minimum local expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 607-618.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:5:p:607-618
    DOI: 10.1080/14697680400000042
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    Cited by:

    1. Emmanuel Gobet & Isaque Pimentel & Xavier Warin, 2020. "Option valuation and hedging using asymmetric risk function: asymptotic optimality through fully nonlinear Partial Differential Equations," Post-Print hal-01761234, HAL.
    2. Lixin Wu & Min Dai, 2009. "Pricing jump risk with utility indifference," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 177-186.
    3. Ramos, Antônio M.T. & Carvalho, J.A. & Vasconcelos, G.L., 2016. "Exponential model for option prices: Application to the Brazilian market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 161-168.
    4. repec:hal:wpaper:hal-01761234 is not listed on IDEAS
    5. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2023. "Backward Hedging for American Options with Transaction Costs," Papers 2305.06805, arXiv.org, revised Jun 2023.
    6. Emmanuel Gobet & Isaque Pimentel & Xavier Warin, 2020. "Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations," Finance and Stochastics, Springer, vol. 24(3), pages 633-675, July.

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