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- Title
A Fully Coupled Solution Algorithm for Pricing Options with Complex Barrier Structures.
- Authors
Zili Zhu; de Hoog, Frank
- Abstract
In financial engineering, the Crank-Nicolson approach of time-stepping is a popular and standard numerical method for solving the Black-Scholes equation. The temporal term in the Black-Scholes equation is discretized through central finite-differencing, and the implementation of Crank-Nicolson approach is straight forward. In this article, we present a very different numerical method for solving the Black-Scholes equation. Instead of using the Crank-Nicolson-style time-stepping scheme, we solve the equation as a fully coupled equation in the time-direction. The numerical results in this article indicate that such numerical schemes are actually more stable and more accurate than the Crank-Nicolson method, particularly when the time-step size is large. Two main advantages of using the fully coupled numerical scheme are 1) the step size for time discretization can be non-uniform at different asset price levels (for example, more refined mesh nodes can be distributed in areas where option values change rapidly in both the space and the time directions); 2) complex barrier structures can be naturally and easily handled with high accuracy and without the need for any extrapolation/interpolation (for example when barrier levels change discontinuously).
- Subjects
PRICING; OPTION value; EQUATIONS; FINANCIAL engineering; ASSETS (Accounting); PRICE levels; FINANCIAL markets
- Publication
Journal of Derivatives, 2010, Vol 18, Issue 1, p9
- ISSN
1074-1240
- Publication type
Article
- DOI
10.3905/jod.2010.18.1.009