6533b857fe1ef96bd12b3ac5

RESEARCH PRODUCT

Iterative Methods for Pricing American Options under the Bates Model

Lina Von SydowSanttu SalmiJari ToivanenJari Toivanen

subject

ta113Mathematical optimizationStochastic volatilityDiscretizationIterative methodComputer scienceFinite difference methodLinear complementarity problemIterative methodQuadrature (mathematics)Multigrid methodFixed-point iterationBates modelLinear complementarity problemGeneral Earth and Planetary SciencesPartial derivativeAmerican optionGeneral Environmental Science

description

We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG method leads to better scalability than the projected SOR (PSOR) method when the discretization is refined. peerReviewed

yearjournalcountryeditionlanguage
2013-01-01Procedia Computer Science
10.1016/j.procs.2013.05.279http://dx.doi.org/10.1016/j.procs.2013.05.279