Numerical Solution For Fractional Black-Scholes Model of American Put Option Pricing
کد مقاله : 1152-FEMATH
1رباب کلانتری *، 2صداقت شهمراد
1دانشگاه تبریز
2هیات علمی
چکیده مقاله:
Abstract. In this paper, we introduce a mathematical modelingnof American put option pricing under the Fractional Black-Scholesnmodel, which leads to a fractional partial differential equation withnfree boundary condition (the American option is an option thatncould be exercised at any time during the life of option). Thennthe free boundary (optimal exercise boundary) that is unknown, isnfound by using the quasi-stationary method that cause the Americannput option pricing problem to be a solvable boundary valuenproblem. In continuation we use a finite difference method for thenderivatives with respect to stock price, Gr¨unwal Letnikov approximationnfor derivatives with respect to time variable and reachna fractional finite difference problem. We show that the set upnfractional finite difference problem is stable and convergent. Wenalso show that the numerical result satisfy the physical conditionsnof American put option pricing under the Fractional Black-Scholesn(FBS) model.
کلیدواژه ها:
Fractional Differential Equation‎, ‎American Option Pricing‎, ‎Finite Difference‎.
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