Finance and Stochastics manuscript No. (will be inserted by the editor) Representation Formulas for Malliavin Derivatives of Diffusion Processes ? J´ erˆ ome Detemple 1 , Ren´ e Garcia 2 , Marcel Rindisbacher 3 1 Boston University School of Management, Boston, MA, 02215, USA, and CIRANO, Montr´ eal H3A2A5, Canada e-mail: detemple@bu.edu 2 Universit´ e de Montr´ eal and CIREQ, Montr´ eal H3C3J7, Canada, and CIRANO, Montr´ eal H3A2A5, Canada e-mail: rene.garcia@umontreal.ca 3 J. L. Rotman School of Management, Toronto M5S3E6, Canada, and CIRANO, Montr´ eal H3A2A5, Canada e-mail: rindisbm@rotman.utoronto.ca received: February 2002; accepted: September 2004 Abstract We provide new representation formulas for Malliavin deriva- tives of diffusions, based on a transformation of the underlying processes. Both the univariate and the multivariate cases are considered. First order as well as higher order Malliavin derivatives are characterized. Numerical illustrations of the benefits of the transformation are provided. Key words Malliavin derivatives, Doss transformation, multivariate dif- fusions Mathematics Subject Classification (1991): 60H07, 60J60, 65C05 JEL Classification: G11, G12, G13 1 Introduction Consider a stochastic process Y that satisfies the stochastic differential equation dY t = μ(t, Y t )dt + σ(t, Y t )dW t ; Y 0 given (1.1) ? Financial support from the Network of Centers of Excellence (MITACS) is gratefully acknowledged. The second author is grateful to Hydro-Qu´ ebec and the Bank of Canada for financial support. Correspondence to : Ren´ e Garcia, Universit´ e de Montr´ eal, CP 6128, Succ. Centre- ville, 3150 rue Jean Brillant, Montr´ eal, Qu´ ebec, H3C3J7, Canada, T´ el: (514) 343- 5960, Fax: (514) 343-5831