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Option pricing and hedging with minimum expected shortfall

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Author Info
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.

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Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500029.

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Date of creation: Aug 2003
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Publication status: Forthcoming in QF
Handle: RePEc:sfi:sfiwpa:500029

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

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  1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 4(4), pages 727-52. [Downloadable!] (restricted)
  2. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(1), pages 113-47.
  3. 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. [Downloadable!]
  4. L. Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor and Francis Journals, vol. 2(6), pages 415-431, June. [Downloadable!] (restricted)
  5. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November. [Downloadable!] (restricted)
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  6. A.A. Dragulescu & V.M. Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor and Francis Journals, vol. 2(6), pages 443-453, June. [Downloadable!] (restricted)
  7. Adrian A. Dragulescu & Victor M. Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance Papers cond-mat/0203046, arXiv.org, revised Nov 2002. [Downloadable!]
  8. 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 637-54, May-June. [Downloadable!] (restricted)
  9. A. Dragulescu & V. M. Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Computing in Economics and Finance 2002 127, Society for Computational Economics.
  10. 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. [Downloadable!]
  11. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December. [Downloadable!] (restricted)
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