On the Solution of Fractional Option Pricing Model by Convolution Theorem
The classical Black-Scholes equation driven by Brownian motion has no memory, therefore it is proper to replace the Brownian motion with fractional Brownian motion (FBM) which has long-memory due to the presence of the Hurst exponent. In this paper, the option pricing equation modeled by fractional Brownian motion is obtained. It is further reduced to a one-dimensional heat equation using Fourier transform and then a solution is obtained by applying the convolution theorem.
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