The Stochastically Subordinated Log Normal Process Applied to Financial Time Series and Option Pricing

Author

David Edelman and Thomas Gillespie

Status

Research Report 97-13
Date: 28 April 1997

Abstract

The method of stochastic subordination, or random time indexing, has been recently applied to Wiener process price processes to model financial returns. Previous emphasis in stochastic subordination models has involved explicitly identifying the subordinating process with an observable quantity such as number of trades. In contrast, the approach taken here does not depend on the specific identification of the subordinated time variable, but rather assumes a class of time models and estimates parameters from data. In addition, a simple Markov process is proposed for the characteristic parameter of the subordinating distribution to explain the significant autocorrelation of the squared returns. It is shown in particular, that the proposed model, while containing only a few more parameters than the commonly used Wiener process models, fits selected financial time series particularly well, characterising the autocorrelation structure and heavy tails, as well as preserving the desirable self-similarity structure present in popular chaos-theoretic models, and the existence of risk-neutral measures necessary for objective derivative valuation.

Key phrases

finance. derivative. stochastic subordination. option pricing.

AMS Subject Classification (1991)

Primary: 90A19
Secondary: 90A09,62M10,90A20

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