A NUMERICAL METHOD TO COMPUTE THE VOLATILITY
OF THE FRACTIONAL BROWNIAN MOTION IMPLIED
BY AMERICAN OPTIONS
OF THE FRACTIONAL BROWNIAN MOTION IMPLIED
BY AMERICAN OPTIONS
Abstract. We develop a highly efficient approach to compute the volatility of the Fractional Brownian Motion (FBM) implied by American options. To this aim, the theoretical values of American option prices under the FBM are calculated using a finite difference scheme enhanced by a space-time Richardson extrapolation procedure. Such an approach, which is coupled with a suitable optimization algorithm, turns out to be very accurate and fast. The practical performances of the method proposed are demonstrated by applying it to the time-series of several stocks belonging to the Italian FTSE-All Share.
AMS Subject Classification: 65B05, 65N06, 91G60, 91G80
Key Words and Phrases: fractional Brownian Motion, option pricing, implied volatility, finite difference method, Richardson extrapolation
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DOI: 10.12732/ijam.v26i2.7
Volume: 26
Issue: 2
Year: 2013
