| تعداد نشریات | 60 |
| تعداد شمارهها | 2,040 |
| تعداد مقالات | 16,469 |
| تعداد مشاهده مقاله | 43,652,943 |
| تعداد دریافت فایل اصل مقاله | 24,822,571 |
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 | ||
|
[1] R. Mertonr, Continuous-Time Finance, 1st ed.; Blackwell: Oxford, UK, (1990). [2] E. Eberlein, F.E. Benth, V.A. Kholodnyi, P. Laurence, Fourier-Based Valuation Methods in Mathematical Finance. In Quantitative Energy Finance, Eds.; Springer: Berlin/Heidelberg, Germany, (2014) pp. 85-114. [3] R.A. Alijedhi, A. Kilicman, Fractional partial differential equations associated with Levy stable process, Mathematics, (2020) 8, 508; doi:10.3390/math8040508. [4] W. Chen, X. Xu, S.P. Zhu, Analytical pricing European-style option under the modi ed Black-Scholes equation with a partial fractional derivative, Quartely Appl. Math (2014) 72: 597-611. [5] R.A. Alijedhi, A. Kilicman, Financial Applications on Fractional Levy Stochastic Processes, Fractal and Fractional, (2022) 2022, 6, 278. https://doi.org/10.3390/fractalfract6050278. [6] S.L.Wang, Y.F. Yang, Y.H. Zeng, The Adjoint Method for the Inverse Problem of Option Pricing, Mathematical Problems in Engineering, (2014) http://dx.doi.org/10.1155/2014/314104. [7] H. Egger, H.W. Engl, Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates, Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, (2004) [8] I. Bouchouev, V. Isakov, Uniqueness, stability and numerical methods for the inverse problem that arises in nancial markets, Inverse Problems, (1999) 15:R95-116. [9] T. Hein, B. Hofmann, On the nature of ill-posedness of an inverse problem in option pricing, Inverse Problems, (2003) 19:1319-1338. [10] Y. Jin, J. Wang, S. Kim, Y. Heo, C. Yoo, Y. Kim, J. KIm and D. Jeong, Reconstruction of the Time-Dependent Volatility Function Using the BlackScholes Model, Discrete Dynamics in Nature and Society, (2018). [11] S. Singh, V. Patel, V. Singh, Application of wavelet collocation method for hyperbolic partial differential equations via matrices, Applied Mathematics and Computation, (2018) 320: 407-424. [12] S. Shen, F. Liu, J. Chen, I. Turner, V. Anh, Numerical techniques for the variable order time fractional diffusion equation, Appl. Math. Comput. (2012) 218: 1086110870. [13] M.N. Ozisik, H. R. B. Orlande, Inverse Heat Transfer, Fundamentals and Applications, NewYork: Taylor Franscis, 2000. | ||
|
آمار تعداد مشاهده مقاله: 252 تعداد دریافت فایل اصل مقاله: 313 |
||