Tridiagonal implicit method to evaluate European and American options under infinite activity Lévy models

Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

“…On the other hand, for the approximation of the integral part of (7), instead of using the trapezoidal rule like in [14,16,20], we use a composite four-point integration formula of open type because of the higher order approximation of this rule [28, pp. 92-93].…”

“…In [20], a three-time-level finite difference method is proposed showing a second order convergence rate in the numerical experiments for infinite activity models. However, the authors in [20] focus the interest on computational issues more than the numerical analysis.…”

“…The PIDE valuating the option price presents a differential part with reaction, convection, and diffusion terms, while the nonlocal integral part is extended over an infinite or semi-infinite interval. Several finite difference (FD) schemes have been proposed to solve numerically these PIDE problems [11][12][13][14][15][16][17][18][19][20]. In order to implement FD methods, there are many challenges to face such as how to treat the unbounded domain for the spatial variable and the possible singularity of the kernel of the integral term.…”

Finite Difference Schemes for Option Pricing under Stochastic Volatility and Lévy Processes: Numerical Analysis and Computing

“…Many authors used the finite difference (FD) schemes for solving these PIDE problems [2,4,5,17,25,54,74,75,82,85,87]. Dealing with FD methods for such PIDEs, the following challenges should be addressed.…”

“…In [54] an efficient three time-level finite difference scheme is proposed for the infinite activity Lévy model. Second order convergence rate are shown in numerical experiments although the numerical analysis of the method is not developed.…”