Using Bernstein and Legendre Multi-Scaling Functions and Ritz Galerkin method to solve Black-Scholes equation
کد مقاله : 1077-FEMATH-FULL (R1)
1نازنین تفاخری *، 2محمود بهروزی فر، 2حمزه آگاهی
2استاد در دپارتمان ریاضی دانشگاه صنعتی نوشیروانی
چکیده مقاله:
Stochastic partial differential equations (SPDEs) provide a quantitative description for mathematical models in areas such as finance. They are essentially partial differential equations that have random forcing terms and coefficients; They can be exceedingly difficult to solve. Most of these equations do not have analytical solution, so it is important to find a approximate solution for them.nA numerical method for solving Black-Scholes partial differential equation based on Bernstein and Shifted-Legendre multi-scaling approximation is proposed. We convert the European option prices under Black-Scholes model to heat equation by using the change of variables. By considering these properties and applying the forward Euler and Ritz Galerkin method, Black-Scholes equation is reduced to algebraic equations and Finally, we check the obtained results of two polynomials with analytic solution with Mathematica software and compare these two methods when increasing parameter k , M and L. Plots show that both approximations are acceptable and applicable.
کلیدواژه ها:
Black-Scholes equation, Eropean option price, Bernstein polynomial,Shifted Legendre polynomial, Ritz Galerkin method.
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