A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivatives

Daniel Conus; Mackenzie Wildman

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arXiv · 1608.03428

A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivatives

Daniel Conus·Mackenzie Wildman

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Abstract

Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial market. We present the development, testing, and implementation of a simplified alternative to using fractional Brownian motion for pricing derivatives. By relaxing the assumption of past independence of Brownian motion but retaining the Markovian property, we are developing a competing model that retains the mathematical simplicity of the standard Black-Scholes model but also has the improved accuracy of allowing for past dependence. This is achieved by replacing Black-Scholes' underlying process, Brownian motion, with a particular Gaussian Markov process, proposed by Vladimir Dobri\'{c} and Francisco Ojeda.

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Daniel Conus, Mackenzie Wildman. 2016-08-11. A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivatives. https://arxiv.org/abs/1608.03428

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