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.
Ballestra, L., Cecere, L. (2013). A NUMERICAL METHOD TO COMPUTE THE VOLATILITY OF THE FRACTIONAL BROWNIAN MOTION IMPLIED BY AMERICAN OPTIONS. INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS, 26(2), 203-220 [10.12732/ijam.v26i2.7].
A NUMERICAL METHOD TO COMPUTE THE VOLATILITY OF THE FRACTIONAL BROWNIAN MOTION IMPLIED BY AMERICAN OPTIONS
BALLESTRA, LUCA VINCENZO;
2013
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
