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Proceedings Paper

Path integrals in fluctuating markets with a non-Gaussian option pricing model
Author(s): Frederic D. R. Bonnet; John van der Hoek; Andrew Allison; Derek Abbott
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Paper Abstract

It is well established that volatility has a memory of the past, moreover it is found that volatility correlations are long ranged. As a consequence the volatility cannot be characterized by a single correlation time. Recent empirical work suggests that the volatility correlation functions of various assets actually decay as a power law. In this paper we show that it is possible to derive the path integral for a non-Gaussian option pricing model that can capture fat-tails. We aim to find the most probable path that contributes to the action functional, that describes the dynamics of the entire system, by finding local minima. We obtain a second order differential equation for the functional return. This paper reviews our current progress and the remaining open questions.

Paper Details

Date Published: 23 May 2005
PDF: 20 pages
Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); doi: 10.1117/12.618664
Show Author Affiliations
Frederic D. R. Bonnet, The Univ. of Adelaide (Australia)
John van der Hoek, The Univ. of Adelaide (Australia)
Andrew Allison, The Univ. of Adelaide (Australia)
Derek Abbott, The Univ. of Adelaide (Australia)

Published in SPIE Proceedings Vol. 5848:
Noise and Fluctuations in Econophysics and Finance
Derek Abbott; Jean-Philippe Bouchaud; Xavier Gabaix; Joseph L. McCauley, Editor(s)

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