| A Stable and Convergent Non-Standard Finite Difference Method for Fractional Black-Scholes Model of Digital Put Option Pricing |
| کد مقاله : 1016-FEMATH5-FULL (R1) |
| نویسندگان |
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رباب کلانتری *1، صداقت شهمراد2 1تهران خیابان آزادی بلوار استاد معین کوچه فردوس پلاک 5 واحد 3 2هیئت علمی دانشگاه تبریز |
| چکیده مقاله |
| Firstly, we introduce the mathematical model of digital put option pricing under the Fractional Black - Scholes model. Following this, we introduce the the digital option pricing condition in Fractional Black - Scholes , then we explain non - standard Finite difference method and non - standard Gr "{u} nwald Letnikov approximation and use these approximations for Stock and time fractional term in Fractional Black - Scholes model to reach a fractional non - standard finite difference problem. We show that the proposed fractional non - standard finite difference scheme is stable and convergent. Continuously, we show that non - standard finite difference (NSFD) method is more stable and more convergence than standard finite difference method in Fractional Black - Scholes model as numerical. Uniqueness of the approximate solution is also proved. We also show that numerical results satisfy the physical conditions of digital put option pricing under the Fractional Black - Scholes (FBS) model. |
| کلیدواژه ها |
| Fractional Differential Equation; Digital Option Pricing; Non-Standard Finite Difference Method; Interpolation Method. |
| وضعیت: پذیرفته شده برای ارائه شفاهی |