We propose the use of the meshfree radial basis point interpolation (RBPI) to solve the Black-Scholes model for European and American options. The RBPI meshfree method offers several advantages over the more conventional radial basis function approximation, nevertheless it has never been applied to option pricing, at least to the very best of our knowledge. In this paper the RBPI is combined with several numerical techniques, namely: an exponential change of variables, which allows us to approximate the option prices on their whole spatial domain, a mesh refinement algorithm, which turns out to be very suitable for dealing with the non-smooth options' payoff, and an implicit Euler Richardson extrapolated scheme, which provides a satisfactory level of time accuracy. Finally, in order to solve the free boundary problem that arises in the case of American options three different approaches are used and compared: the projected successive overrelaxation method (PSOR), the Bermudan approximation, and the penalty approach. Numerical experiments are presented which demonstrate the computational efficiency of the RBPI and the effectiveness of the various techniques employed.
Pricing European and American options by radial basis point interpolation / Rad, Jamal Amani; Parand, Kourosh; Ballestra, Luca Vincenzo. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - STAMPA. - 251:(2015), pp. 363-377. [10.1016/j.amc.2014.11.016]
Pricing European and American options by radial basis point interpolation
BALLESTRA, LUCA VINCENZO
2015
Abstract
We propose the use of the meshfree radial basis point interpolation (RBPI) to solve the Black-Scholes model for European and American options. The RBPI meshfree method offers several advantages over the more conventional radial basis function approximation, nevertheless it has never been applied to option pricing, at least to the very best of our knowledge. In this paper the RBPI is combined with several numerical techniques, namely: an exponential change of variables, which allows us to approximate the option prices on their whole spatial domain, a mesh refinement algorithm, which turns out to be very suitable for dealing with the non-smooth options' payoff, and an implicit Euler Richardson extrapolated scheme, which provides a satisfactory level of time accuracy. Finally, in order to solve the free boundary problem that arises in the case of American options three different approaches are used and compared: the projected successive overrelaxation method (PSOR), the Bermudan approximation, and the penalty approach. Numerical experiments are presented which demonstrate the computational efficiency of the RBPI and the effectiveness of the various techniques employed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.