A numerical method for solving the underly- ing price problem driven by a fractional Levy process

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 manage- ment, 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 op- tions. 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 effective- ness of the methodology used.