MPS-RR 1999-19
June 1999

Risk neutral densities of the `Christmas tree' type

Jens Ledet Jensen

Niels Væver Hartvig, Jan Pedersen

Abstract

From observed bid and ask prices of European call and put options we estimate the risk neutral density of a stock at some future time t > 0. We restrict attention to a class of densities with heavy tails and use a Bayesian formulation in order to study the variation in the distributions fitting the data. From the fitted risk neutral density we also consider the inverse problem of finding the volatility in a diffusion model for the price process. Finally, we apply our methods to data on the S&P 500 index.

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