Recovering Nonlinear Dynamics from Option Prices
University of Geneva
University of Geneva - HEC; Swiss Finance Institute
affiliation not provided to SSRN
June 14, 2011
Paris December 2011 Finance Meeting EUROFIDAI - AFFI
Using the wavelet-Galerkin method for solving partial integro-differential equations, we derive an implement computationally efficient formula for pricing European options on assets driven by multivariate jump-diffusions. This pricing formula is then used to solve the inverse problem of estimating the corresponding 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 regularization 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.
Number of Pages in PDF File: 34
Keywords: Inverse and ill-posed problem, volatility dynamics, option valuationworking papers series
Date posted: October 14, 2011
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