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http://dx.doi.org/10.4134/BKMS.b150731

OPTION PRICING UNDER GENERAL GEOMETRIC RIEMANNIAN BROWNIAN MOTIONS

Zhang, Yong-Chao (School of Mathematics and Statistics Northeastern University at Qinhuangdao)

Publication Information

Bulletin of the Korean Mathematical Society / v.53, no.5, 2016 , pp. 1411-1425 More about this Journal

Abstract

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

Keywords

geometric Riemannian Brownian motion; Stratonovich integral; option pricing;

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