2016/12/01 by Balajewicz, Maciej, Toivanen, Jari
#Computational Engineering #Computational Finance (q-fin.CP) #FOS: Computer and information sciences #FOS: Economics and business #Finance #and Science (cs.CE)
paper · doi:10.48550/arxiv.1612.00402
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a given model parameter variation range.