A class of risk neutral densities with heavy tails

Niels VÖver Hartvig (), Jens Ledet Jensen () and Jan Pedersen ()
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Niels VÖver Hartvig: Department of Theoretical Statistics, Department of Mathematical Sciences and MaPhySto, Ny Munkegade, DK-8000 Aarhus C, Denmark Manuscript
Jens Ledet Jensen: Department of Theoretical Statistics, Department of Mathematical Sciences and MaPhySto, Ny Munkegade, DK-8000 Aarhus C, Denmark Manuscript
Jan Pedersen: Department of Theoretical Statistics, Department of Mathematical Sciences and MaPhySto, Ny Munkegade, DK-8000 Aarhus C, Denmark Manuscript

Finance and Stochastics, 2001, vol. 5, issue 1, 115-128

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. Heavy tails are here meant in the intuitive sense of being heavier than the tails of a normal distribution. 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.

Keywords: Christmas tree densities; risk neutral density; Markov chain Monte Carlo; inverse problems; diffusion model (search for similar items in EconPapers)
Date: 2001-01-10
Note: received: June 1999 / final version received: March 2000
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Citations: View citations in EconPapers (3)

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