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Ana M. Monteiro (amonteirofe.uc.pt) Abstract: We present a new approach to estimate the riskneutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and determine the corresponding density function, is a convex quadratic or semidefinite programming problem, depending on the formulation. Both of these problems can be efficiently solved by numerical optimization software. In the quadratic programming formulation the positivity of the riskneutral pdf is heuristically handled by posing linear inequality constraints at the spline nodes. In the other approach, this property of the riskneutral pdf is rigorously ensured by using a semidefinite programming characterization of nonnegativity for polynomial functions. We tested our approach using data simulated from BlackScholes option prices and using market data for options on the S&P 500 Index. The numerical results we present show the effectiveness of our methodology for estimating the riskneutral probability density function. Keywords: option pricing, riskneutral density estimation, cubic splines, quadratic programming, semidefinite programming Category 1: Applications  OR and Management Sciences (Finance and Economics ) Category 2: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 3: Nonlinear Optimization (Quadratic Programming ) Citation: Preprint 0422 Department of Mathematics, University of Coimbra, Portugal July 2004 Download: [PDF] Entry Submitted: 07/22/2004 Modify/Update this entry  
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