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Option pricing and hedging with minimum expected shortfall

Author

Listed:
  • Benoit Pochard

    (Centre de mathematiques appliquees, Ecole Polytechnique, Palaiseau, FRANCE)

  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

Abstract

We propose a versatile Monte-Carlo method for pricing and hedging options when markets are inco;plete, for an arbitrary risk criterion (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 to significantly reduce extreme risks, and generically leads to low Gamma hedging. Similarly, the inclusion of transaction costs reduces the Gamma of the optimal strategy.

Suggested Citation

  • Benoit Pochard & Jean-Philippe Bouchaud, 2003. "Option pricing and hedging with minimum expected shortfall," Science & Finance (CFM) working paper archive 500029, Science & Finance, Capital Fund Management.
    • Handle: RePEc:sfi:sfiwpa:500029
    as

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    References listed on IDEAS

    as
    1. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 443-453.
    2. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    3. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    4. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    5. Benoit Pochard & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Science & Finance (CFM) working paper archive 0204047, Science & Finance, Capital Fund Management.
    6. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    7. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    8. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    9. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    10. Marc Potters & Jean-Philippe Bouchaud & Dragan Sestovic, 2000. "Hedged Monte-Carlo: low variance derivative pricing with objective probabilities," Science & Finance (CFM) working paper archive 500031, Science & Finance, Capital Fund Management.
    11. repec:cdl:anderf:qt43n1k4jb is not listed on IDEAS
    12. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    13. 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.
    14. Benoit Pochart & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 303-314.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    16. Jaume Masoliver & Josep Perelló, 2002. "A Correlated Stochastic Volatility Model Measuring Leverage And Other Stylized Facts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 541-562.
    17. Potters, Marc & Bouchaud, Jean-Philippe & Sestovic, Dragan, 2001. "Hedged Monte-Carlo: low variance derivative pricing with objective probabilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 517-525.
    18. repec:dau:papers:123456789/1392 is not listed on IDEAS
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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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