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It is demonstrated that approximation of the solution of the Black-Scholes partial differential equation by using a finite difference method is equivalent to approximating the diffusion process by a jump process and therefore the finite difference approximation is a type of numerical integration. In particular, we establish that the explicit finite difference approximation is equivalent to approximating to diffusion process by a jump process, initially introduced by Cox and Ross, while the implicit finite difference approximation amounts to approximating the diffusion process by a more general type of jump process. This work has been introduced by Brennan and Schwartz, The Journal of Financial and Quantitative Analysis,  (1978).
Paul W. Eloe
Primary Advisor's Department
Stander Symposium poster
Zhang, Dan, "A Synthesis of finite difference methods and the jump process arising in the pricing of Contingent Claim" (2012). Stander Symposium Posters. 189.