Electronic Communications in Probability

Computation of Greeks for Barrier and Lookback Options Using Malliavin Calculus

Emmanuel Gobet and Arturo Kohatsu-Higa

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Abstract

In this article, we consider the numerical computations associated to the Greeks of barrier and lookback options, using Malliavin calculus. For this, we derive some integration by parts formulae involving the maximum and minimum of a one dimensional diffusion. Numerical tests illustrate the gain of accuracy compared to classical methods.

Article information

Source
Electron. Commun. Probab., Volume 8 (2003), paper no. 6, 51-62.

Dates
Accepted: 12 May 2003
First available in Project Euclid: 18 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463608890

Digital Object Identifier
doi:10.1214/ECP.v8-1069

Mathematical Reviews number (MathSciNet)
MR1987094

Zentralblatt MATH identifier
1061.60054

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60J60: Diffusion processes [See also 58J65] 65C05: Monte Carlo methods

Keywords
Barrier and lookback options. Option sensitivities. Malliavin calculus

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Gobet, Emmanuel; Kohatsu-Higa, Arturo. Computation of Greeks for Barrier and Lookback Options Using Malliavin Calculus. Electron. Commun. Probab. 8 (2003), paper no. 6, 51--62. doi:10.1214/ECP.v8-1069. https://projecteuclid.org/euclid.ecp/1463608890


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References

  • E. Benhamou, An appplication of Malliavin calculus to continuous time Asian Options'Greeks, Technical report, London School of Economics, (2000) (preprint).
  • M. Broadie and P. Glasserman, Estimating security price derivatives using simulation, Management Science 42(2), (1996) 269–285.
  • P. Cattiaux, Calcul stochastique et opérateurs dégénérés du second ordre - II. Problème de Dirichlet, Bull. Sc. Math., 2ème série 115, (1991) 81–122.
  • E. Fournié, J.M. Lasry, J. Lebuchoux, P.L. Lions, and N. Touzi, Applications of Malliavin calculus to Monte Carlo methods in finance, Finance and Stochastics 3, (1999) 391–412.
  • E. Fournié, J.M. Lasry, J. Lebuchoux, and P.L. Lions., Applications of Malliavin calculus to Monte Carlo methods in finance, II, Finance and Stochastics 5, (2001) 201–236.
  • A.M. Garsia, E. Rodemich, and H.Jr. Rumsey, A real variable lemma and the continuity of paths of some gaussian processes, Indiana University Mathematics Journal, 20(6), (1970) 565–578.
  • P. Glasserman and D.D. Yao, Some guidelines and guarantees for common random numbers. Management Science, 38(6), (1992) 884–908.
  • I. Karatzas and S.E. Shreve. Brownian motion and stochastic calculus, Second Edition, Springer Verlag, (1991).
  • P. L'Ecuyer and G. Perron, On the convergence rates of IPA and FDC derivative estimators, Oper. Res., 42(4), (1994) 643–656.
  • D. Nualart. Malliavin calculus and related topics, Springer Verlag, (1995).
  • D. Nualart and J. Vives, Absolute continuity of the law of the maximum of a continuous process, C. R. Acad. Sci., Paris, 307(7), (1988) 349–354.