23 May 2005 Path integrals in fluctuating markets with a non-Gaussian option pricing model
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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.
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Frederic D. R. Bonnet, Frederic D. R. Bonnet, John van der Hoek, John van der Hoek, Andrew Allison, Andrew Allison, Derek Abbott, 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); doi: 10.1117/12.618664; https://doi.org/10.1117/12.618664
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