Numerical Approximation of the Black - Scholes Equations : A Practical Experience by Dylan Connor
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چکیده
Numerical Approximation of the Black-Scholes Equations: A Practical Experience By Dylan Connor Black and Scholes equations for pricing of derivatives are an interesting and up-to-date topic of research, where both backgrounds in math and finance are fundamentals. In this work we aim at experiencing the mathematical approach and the numerical approximation of this differential problem. We will assume these equations to be a reliable model and will work on their numerical approximation with a mixed finite elements(FE)/finite differences (FD) approach. More precisely, we will use the mathematically well-established Finite Element Method (FEM) for the underlying price dependence, while time dependence will be discretized with the Finite Difference Method (FDM). The ultimate purpose of the work is to earn sensitivity when using numerical tools in financial mathematics, with particular attention to the critical analysis of the results. This includes an extensive error analysis and appropriate visualization of the results. This will allow us to comment on the practicality of numerical mathematics used to solve the Black-Scholes equation. Numerical Approximation of the Black-Scholes Equations: A Practical Experience
منابع مشابه
A family of positive nonstandard numerical methods with application to Black-Scholes equation
Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.
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