A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options
سال انتشار: 1400
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 241
فایل این مقاله در 30 صفحه با فرمت PDF قابل دریافت می باشد
- صدور گواهی نمایه سازی
- من نویسنده این مقاله هستم
استخراج به نرم افزارهای پژوهشی:
شناسه ملی سند علمی:
JR_CMDE-9-2_014
تاریخ نمایه سازی: 15 بهمن 1401
چکیده مقاله:
The Black-Scholes equation is one of the most important mathematical models in option pricing theory, but this model is far from market realities and cannot show memory effect in the financial market. This paper investigates an American option based on a time-fractional Black-Scholes equation under the constant elasticity of variance (CEV) model, which parameters of interest rate and dividend yield supposed as deterministic functions of time, and the price change of the underlying asset follows a fractal transmission system. This model does not have a closed-form solution; hence, we numerically price the American option by using a compact difference scheme. Also, we compare the time-fractional Black-Scholes equation under the CEV model with its generalized Black-Scholes model as α = ۱ and β = ۰. Moreover, we demonstrate that the introduced difference scheme is unconditionally stable and convergent using Fourier analysis. The numerical examples illustrate the efficiency and accuracy of the introduced difference scheme.
کلیدواژه ها:
نویسندگان
Maryam Rezaei Mirarkolaei
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
Ahmadreza Yazdanian
Faculty of Finance Sciences Kharazmi University, Tehran, Iran.
Seyed Mahdi Mahmoudi
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Ali Ashrafi
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran