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Nasiri, Tayebeh, Zakeri, Ali, Aminataei, Azim. (1401). A numerical method for solving the underlying price problem driven by a fractional Levy process. سامانه مدیریت نشریات علمی, 2(1), 195-208. doi: 10.22054/jmmf.2022.14573
Tayebeh Nasiri; Ali Zakeri; Azim Aminataei. "A numerical method for solving the underlying price problem driven by a fractional Levy process". سامانه مدیریت نشریات علمی, 2, 1, 1401, 195-208. doi: 10.22054/jmmf.2022.14573
Nasiri, Tayebeh, Zakeri, Ali, Aminataei, Azim. (1401). 'A numerical method for solving the underlying price problem driven by a fractional Levy process', سامانه مدیریت نشریات علمی, 2(1), pp. 195-208. doi: 10.22054/jmmf.2022.14573
Nasiri, Tayebeh, Zakeri, Ali, Aminataei, Azim. A numerical method for solving the underlying price problem driven by a fractional Levy process. سامانه مدیریت نشریات علمی, 1401; 2(1): 195-208. doi: 10.22054/jmmf.2022.14573

A numerical method for solving the underlying price problem driven by a fractional Levy process

Journal of Mathematics and Modeling in Finance
مقاله 11، دوره 2، شماره 1، مهر 2022، صفحه 195-208    اصل مقاله (335.96 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22054/jmmf.2022.14573
نویسندگان
Tayebeh Nasiri1؛ Ali Zakeri* 2؛ Azim Aminataei1
1Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
2Faculty if marhematics, K. N. Toosi University of Technology
چکیده
We consider European style options with risk-neutral parameters and time-fractional Levy diffusion equation of the exponential option pricing model in this paper. In a real market, volatility is a measure of the quantity of inflation in asset prices and changes. This makes it essential to accurately measure portfolio volatility, asset valuation, risk management, and monetary policy. We consider volatility as a function of time. Estimating volatility in the time-fractional Levy diffusion equation is an inverse problem. We use a numerical technique based on Chebyshev wavelets to estimate volatility and the price of European call and put options. To determine unknown values, the minimization of a least-squares function is used. Because the obtained corresponding system of linear equations is ill-posed, we use the Levenberg-Marquardt regularization technique. Finally, the proposed numerical algorithm has been used in a numerical example. The results demonstrate the accuracy and effectiveness of the methodology used.
کلیدواژه‌ها
European options؛ Time-fractional Levy diffusion equation؛ Volatility؛ Chebyshev wavelets؛ Levenberg-Marquardt regularization
مراجع
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