Conditional Density Models for Asset Pricing

23 Pages Posted: 6 Nov 2010 Last revised: 9 Nov 2011

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

L. P. Hughston

University of London - Department of Mathematics

Andrea Macrina

University College London; University of Cape Town (UCT)

Date Written: August 15, 2010

Abstract

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master equation" for the dynamics of the conditional probability density is derived and expressed in integral form. By a "model" for the conditional density process we mean a solution to the master equation along with the specification of (a) the initial density, and (b) the volatility structure of the density. The volatility structure is assumed at any time and for each value of the argument of the density to be a functional of the history of the density up to that time. This functional determines the model for the conditional density. In practice one specifies the functional modulo sufficient parametric freedom to allow for the input of additional option data apart from that implicit in the initial density. The scheme is sufficiently exible to allow for the input of various types of data depending on the nature of the options market and the class of valuation problem being undertaken. Various examples are studied in detail, with exact solutions provided in some cases.

Keywords: Option Pricing, Implied Volatility, Breeden-Litzenberger Equation, Volatility Surface, Information-Based Asset Pricing

JEL Classification: C60, C63, G12, G13

Suggested Citation

Filipovic, Damir and Hughston, Lane P. and Macrina, Andrea, Conditional Density Models for Asset Pricing (August 15, 2010). Swiss Finance Institute Research Paper No. 10-44. Available at SSRN: https://ssrn.com/abstract=1702871 or http://dx.doi.org/10.2139/ssrn.1702871

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Lane P. Hughston

University of London - Department of Mathematics ( email )

Strand
London, WC2R 2LS
United Kingdom

Andrea Macrina

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

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