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Extra-Dimensional Approach to Option Pricing and Stochastic Volatility

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  • Minh Q. Truong

Abstract

The generalized 5D Black-Scholes differential equation with stochastic volatility is derived. The projections of the stochastic evolutions associated with the random variables from an enlarged space or superspace onto an ordinary space can be achieved via higher-dimensional operators. The stochastic nature of the securities and volatility associated with the 3D Merton-Garman equation can then be interpreted as the effects of the extra dimensions. We showed that the Merton-Garman equation is the first excited state, i.e. n=m=1, within a family which contain an infinite numbers of Merton-Garman-like equations.

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  • Minh Q. Truong, 2010. "Extra-Dimensional Approach to Option Pricing and Stochastic Volatility," Papers 1001.4098, arXiv.org, revised Feb 2010.
    • Handle: RePEc:arx:papers:1001.4098
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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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