Computation of Greeks for Barrier and Lookback Options Using Malliavin Calculus

Emmanuel Gobet (Centre de Mathématiques Appliquées)
Arturo Kohatsu-Higa (Universitat Pompeu Fabra)

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.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 51 - 62

Publication Date: May 12, 2003

DOI: 10.1214/ECP.v8-1069

References

  1. E. Benhamou, An appplication of Malliavin calculus to continuous time Asian Options'Greeks, Technical report, London School of Economics , (2000) (preprint). Math. Review number not available.
  2. M. Broadie and P. Glasserman, Estimating security price derivatives using simulation, Management Science 42(2), (1996) 269--285. Math. Review number not available.
  3. P. Cattiaux, Calcul stochastique et opérateurs dégénérés du second ordre - II. Problème de Dirichlet, Bull. Sc. Math., 2ème série 115, (1991) 81--122. MR92f:60099
  4. 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. MR2002e:91062
  5. 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. MR2002e:91063
  6. 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. MR42#2534
  7. P. Glasserman and D.D. Yao, Some guidelines and guarantees for common random numbers. Management Science, 38(6), (1992) 884--908. Math. Review number not available.
  8. I. Karatzas and S.E. Shreve. Brownian motion and stochastic calculus, Second Edition, Springer Verlag, (1991). MR92h:60127 
  9. P. L'Ecuyer and G. Perron, On the convergence rates of IPA and FDC derivative estimators, Oper. Res., 42(4), (1994) 643--656. Math Review not available.
  10. D. Nualart. Malliavin calculus and related topics , Springer Verlag, (1995). MR96k:60130 
  11. 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. MR89i:60082
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.