Electronic copy available at: http://ssrn.com/abstract=1944051 Recovering Nonlinear Dynamics from Option Prices Alexandre Engulatov ∗ Raul Gonzalez † Olivier Scaillet ‡ This version: June 2011 Preliminary Version Abstract Using the wavelet-Galerkin method for solving partial integro-differential equations, we derive an implement computationally efficient formula for pric- ing European options on assets driven by multivariate jump-diffusions. This pricing formula is then used to solve the inverse problem of estimating the cor- responding risk-neutral coefficient functions of the underlying jump-diffusions from observed option data. The ill-posedness of this estimation problem is proved, and a consistent estimation technique employing Tikhonov regular- ization is proposed. Using S&P 500 Index option data, it is shown that the coefficient functions in a stochastic volatility model with jumps are nonlinear, contrary to the affine specification widely used in the literature. * University of Geneva. e-mail: Alexandre.Engulatov@unige.ch. † University of Geneva. e-mail: Raul.Gonzalez@unige.ch. ‡ University of Geneva and Swiss Finance Institute. e-mail: Olivier.Scaillet@unige.ch. 1