Abstract
Prices of options on two assets following two independent geometric Lévy processes are governed by a 2D fractional Black–Scholes (BS) equation. The discretization of the BS equation yields linear systems with dense system matrices and the numerical solution of them is computationally intensive. In this work, we develop a 2nd-order Crank–Nicolson Alternating Direction Implicit (ADI) method for solving these systems, based on a 2nd-order finite different technique proposed by us. A convergence theory for the method is established. Numerical results are presented to demonstrate the theoretical convergent rate of the ADI method and its computational efficiency.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
