Premium
Robust spectral method for numerical valuation of european options under Merton's jump‐diffusion model
Author(s) -
Pindza E.,
Patidar K.C.,
Ngounda E.
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21864
Subject(s) - mathematics , spectral method , collocation method , jump diffusion , quadrature (astronomy) , partial differential equation , collocation (remote sensing) , nyström method , numerical integration , numerical analysis , jump , ordinary differential equation , differential equation , mathematical analysis , integral equation , computer science , physics , engineering , quantum mechanics , machine learning , electrical engineering
We propose a novel numerical method based on rational spectral collocation and Clenshaw–Curtis quadrature methods together with the “ sinh ” transformation for pricing European vanilla and butterfly spread options under Merton's jump‐diffusion model. Under certain assumptions, such model leads to a partial integro‐differential equation (PIDE). The differential and integral parts of the PIDE are approximated by the rational spectral collocation and the Clenshaw–Curtis quadrature methods, respectively. The application of spectral collocation method to the PIDE leads to a system of ordinary differential equations, which is solved using the implicit–explicit predictor–corrector (IMEX‐PC) schemes in which the diffusion term is integrated implicitly, whereas the convolution integral, reaction, advection terms are integrated explicitly. Numerical experiments illustrate that our approach is highly accurate and efficient for pricing financial options.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1169–1188, 2014