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Description

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, [13] (1978).

Publication Date

4-18-2012

Project Designation

Graduate Research

Primary Advisor

Paul W. Eloe

Primary Advisor's Department

Mathematics

Keywords

Stander Symposium poster

A Synthesis of finite difference methods and the jump process arising in the pricing of Contingent Claim

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