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A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks

  • Eric Benhamou

    (Goldman Sachs International)

This paper presented a new technique for the simulation of the Greeks (i.e. price sensitivities to parameters), efficient for strongly discontinuous payo¤ options. The use of Malliavin calculus, by means of an integration by parts, enables to shift the differentiation operator from the payo¤ function to the diffusion kernel, introducing a weighting function.(Fournie et al. (1999)). Expressing the weighting function as a Skorohod integral, we show how to characterize the integrand with necessary and sufficient conditions, giving a complete description of weighting function solutions. Interestingly, for adapted process, the Skorohod integral turns to be the classical Ito integral.

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File URL: http://128.118.178.162/eps/fin/papers/0212/0212003.pdf
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Paper provided by EconWPA in its series Finance with number 0212003.

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Length: 126 pages
Date of creation: 21 Dec 2002
Date of revision:
Handle: RePEc:wpa:wuwpfi:0212003
Note: Type of Document - PDF; prepared on windows; pages: 126
Contact details of provider: Web page: http://128.118.178.162

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  1. Paul Glasserman & David D. Yao, 1992. "Some Guidelines and Guarantees for Common Random Numbers," Management Science, INFORMS, vol. 38(6), pages 884-908, June.
  2. 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.
  3. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
  4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  5. 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.
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