Premium
Preconditioned iterative methods for fractional diffusion models in finance
Author(s) -
Meng QingJiang,
Ding Deng,
Sheng Qin
Publication year - 2015
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.21948
Subject(s) - mathematics , extrapolation , partial differential equation , partial derivative , monotone polygon , fractional calculus , conjugate gradient method , mathematical optimization , mathematical analysis , geometry
Most recent qualitative models for financial assets assume that the dynamics of underlying equity prices follows a jump or Lévy process. It has been evident that some most intricate characteristics of such dynamics can be captured by CGMY and KoBoL procedures. The prices of financial derivatives with such models satisfy fractional partial differential equations or partial integro‐differential equations. This study focuses at aforementioned fractional equations and discretizes them via a monotone Crank–Nicolson procedure. A spatial extrapolation strategy is introduced to ensure an overall second‐order accuracy in approximations. Preconditioned conjugate gradient normal residual methods are incorporated for solving resulted linear systems. Numerical examples are given to illustrate the accuracy and efficiency of the novel computational approaches implemented. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1382–1395, 2015