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Entropy 2001, 3(5), 300-324; doi:10.3390/e3050300

Some Divergence Properties of Asset Price Models

Department of Mathematical Stochastics, University of Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany
Received: 15 August 2001 / Accepted: 20 December 2001 / Published: 20 December 2001
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Abstract

We consider asset price processes Xt which are weak solutions of one-dimensional stochastic differential equations of the form (equation (2)) Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownian motion. We study properties of the Iα-divergence between the law of the solution Xt and the corresponding drift-less measure (the special case α=1 is the relative entropy). This will be applied to some context in statistical information theory as well as to arbitrage theory and contingent claim valuation. For instance, the seminal option pricing theorems of Black-Scholes and Merton appear as a special case.
Keywords: Iα-divergence; relative entropy; statistical information; equivalent martingale measure; option pricing; Black-Scholes-Merton Iα-divergence; relative entropy; statistical information; equivalent martingale measure; option pricing; Black-Scholes-Merton
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Stummer, W. Some Divergence Properties of Asset Price Models. Entropy 2001, 3, 300-324.

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