Path integrals in fluctuating markets with a non-Gaussian option pricing model

Frederic D. R. Bonnet; John van der Hoek; Andrew Allison; Derek Abbott

doi:10.1117/12.618664

23 May 2005 Path integrals in fluctuating markets with a non-Gaussian option pricing model

Frederic D. R. Bonnet, John van der Hoek, Andrew Allison, Derek Abbott

Proceedings Volume 5848, Noise and Fluctuations in Econophysics and Finance; (2005) https://doi.org/10.1117/12.618664
Event: SPIE Third International Symposium on Fluctuations and Noise, 2005, Austin, Texas, United States

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.

Citation Download Citation

Frederic D. R. Bonnet, John van der Hoek, Andrew Allison, and Derek Abbott "Path integrals in fluctuating markets with a non-Gaussian option pricing model", Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); https://doi.org/10.1117/12.618664

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