Numerical computation of fractional Black-Scholes equation with ‎time-dependent parameters ‎for American options under the CEV model
کد مقاله : 1012-FEMATH5-FULL
نویسندگان:
مریم رضائی میرارکلائی *1، احمد رضا یزدانیان2
1مطهری محله- ک 22 بهمن-بن بست دوم-کد پستی 4764943994
2دانشگاه سمنان
چکیده مقاله:
In this paper, we investigate time- fractional Black- Scholes equation under the constant elasticity of variance (CEV) model for American option pricing which risk- free interest rate and dividend yield assumed as deterministic functions of time and local volatility is a function of underlying asset price. By using finite difference scheme, we obtain numerical approximation of American option. We use two finite difference scheme for the Black- Scholes equation to determine the American option price under CEV model with time- dependent parameters. We get approximation solution of the Black- Scholes equation with time- fractional order derivative and time-integer order derivative by using implicit finite difference method and Crank- Nicolson finite difference method, respectively. Also, we check behavior of American option price relative to the parameters of elasticity factor, fractional order derivative and risk- free interest rate, that option price is increasing or decreasing relative to parameters. The example shows ‎efficiency‎ of the method.
کلیدواژه ها:
CEV model, Time-dependent parameters, Option pricing, American option, Fractional Black-Scholes equation.
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