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Conditional Density Models for Asset Pricing

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  • Damir FILIPOVIC

    (Ecole Polytechnique Fédérale de Lausanne and Swiss Finance Institute)

  • Lane P. HUGHSTON

    (Imperial College London)

  • Andrea MACRINA

    (King's College London and Kyoto University)

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    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 flexible 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.

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    Bibliographic Info

    Paper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 10-44.

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    Length: 26 pages
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    Handle: RePEc:chf:rpseri:rp1044

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    Web page: http://www.SwissFinanceInstitute.ch
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    Related research

    Keywords: option pricing; implied volatility; Breeden-Litzenberger equation; volatility surface; information-based asset pricing.;

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