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Rezaei Mirarkolaei, Maryam, Yazdanian, Ahmadreza, Mahmoudi, Seyed Mahdi, Ashrafi, Ali. (1400). A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options. سامانه مدیریت نشریات علمی, 9(2), 523-552. doi: 10.22034/cmde.2020.36000.1623
Maryam Rezaei Mirarkolaei; Ahmadreza Yazdanian; Seyed Mahdi Mahmoudi; Ali Ashrafi. "A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options". سامانه مدیریت نشریات علمی, 9, 2, 1400, 523-552. doi: 10.22034/cmde.2020.36000.1623
Rezaei Mirarkolaei, Maryam, Yazdanian, Ahmadreza, Mahmoudi, Seyed Mahdi, Ashrafi, Ali. (1400). 'A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options', سامانه مدیریت نشریات علمی, 9(2), pp. 523-552. doi: 10.22034/cmde.2020.36000.1623
Rezaei Mirarkolaei, Maryam, Yazdanian, Ahmadreza, Mahmoudi, Seyed Mahdi, Ashrafi, Ali. A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options. سامانه مدیریت نشریات علمی, 1400; 9(2): 523-552. doi: 10.22034/cmde.2020.36000.1623

A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options

Computational Methods for Differential Equations
مقاله 14، دوره 9، شماره 2، تیر 2021، صفحه 523-552    اصل مقاله (604.75 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.36000.1623
نویسندگان
Maryam Rezaei Mirarkolaei1؛ Ahmadreza Yazdanian* 2؛ Seyed Mahdi Mahmoudi3؛ Ali Ashrafi3
1Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
2Faculty of Finance Sciences Kharazmi University, Tehran, Iran.
3Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
چکیده
‎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 = 1 and β = 0. 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.
کلیدواژه‌ها
CEV model؛ Time-dependent parameters؛ Option pricing؛ American option؛ Fractional BlackScholes equation؛ Compact difference scheme
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