Dynamic Evolution for Risk-Neutral Densities

A. M. Monteiro(amonteirofe.uc.pt)
R. H. Tütüncü(reha.tutuncugs.com)
L. N. Vicente(lnvmat.uc.pt)

Abstract: Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating the evolution of the risk-neutral density in time. Our method uses bicubic splines in order to achieve the desired smoothness for the estimation and an optimization model to choose the spline functions that best fit the price data. Semidefinite programming is employed to guarantee the nonnegativity of the densities. We illustrate the process using synthetic option price data generated using log-normal and absolute diffusion processes as well as actual price data for options on the S&P500 index. We also used the risk-neutral densities that we computed to price exotic options and observed that this approach generates prices that closely approximate the market prices of these options.

Keywords: Risk-neutral density surface, volatility surface, semidefinite programming, option pricing, binary options

Category 1: Applications -- OR and Management Sciences (Finance and Economics )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 3: Nonlinear Optimization (Quadratic Programming )

Citation: Pre-print 08-52, Dept. Mathematics, Univ. Coimbra

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Entry Submitted: 10/28/2008
Entry Accepted: 10/28/2008
Entry Last Modified: 10/28/2008

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