We deal with the problem of pricing barrier options on an underlying described by the mixed fractional Brownian model. To this aim, we consider the initial-boundary value partial differential problem that yields the option price and we derive an integral representation of it in which the integrand functions must be obtained solving Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to solve the integral equations obtained. Numerical simulations reveal that the proposed method is extremely accurate and fast, and performs significantly better than the finite difference method.
Ballestra, L.V., Pacelli, G., Radi, D. (2016). A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion. CHAOS, SOLITONS AND FRACTALS, 87, 240-248 [10.1016/j.chaos.2016.04.008].
A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion
BALLESTRA, LUCA VINCENZO;
2016
Abstract
We deal with the problem of pricing barrier options on an underlying described by the mixed fractional Brownian model. To this aim, we consider the initial-boundary value partial differential problem that yields the option price and we derive an integral representation of it in which the integrand functions must be obtained solving Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to solve the integral equations obtained. Numerical simulations reveal that the proposed method is extremely accurate and fast, and performs significantly better than the finite difference method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
