Bull. Korean Math. Soc. 2016; 53(5): 1411-1425
Online first article August 25, 2016 Printed September 30, 2016
https://doi.org/10.4134/BKMS.b150731
Copyright © The Korean Mathematical Society.
Yong-Chao Zhang
Taishan Road 143
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
MSC numbers: 60H30, 91G20
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