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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-19
June 1999

Risk neutral densities of the `Christmas tree' type


Jens Ledet Jensen

Niels Væver Hartvig, Jan Pedersen


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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This paper has now been published in Finance and Stochastic 5, 115-128 (2001)