A numerical method for solving the underlying price problem driven by a fractional Levy process
عنوان مقاله: A numerical method for solving the underlying price problem driven by a fractional Levy process
شناسه ملی مقاله: JR_JMMF-2-1_011
منتشر شده در در سال 1401
شناسه ملی مقاله: JR_JMMF-2-1_011
منتشر شده در در سال 1401
مشخصات نویسندگان مقاله:
Tayebeh Nasiri - Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
Ali Zakeri - Faculty if marhematics, K. N. Toosi University of Technology
Azim Aminataei - Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
خلاصه مقاله:
Tayebeh Nasiri - Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
Ali Zakeri - Faculty if marhematics, K. N. Toosi University of Technology
Azim Aminataei - Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
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.
کلمات کلیدی: European options, Time-fractional Levy diffusion equation, Volatility, Chebyshev wavelets, Levenberg-Marquardt regularization
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1523435/