Dynamic Modeling and Simulation of Option Pricing Based on Fractional Diffusion Equations with Double Derivatives

The work adopts Caputo fractional derivative, conformable fractional derivative and local fractional derivative to study option pricing problems in fractal financial market. Under local and nonlocal fractional derivatives, space-time fractional diffusion equations of option pricing are established by the replicating portfolios and the theorems of fractional calculus. Option pricing models with double fractional derivatives are dealt with by an enhanced technique of Homotopy perturbation method. Adaptive and analytical approximate pricing formulas are derived. With the help of symbolic computation softwares, the results are tested through the data from China mainland market. Practical examples illustrate the feasibilities and effectiveness of the proposed models. The work tries to employ advanced fractional calculus to establish new option pricing models and provide new tools for financial derivatives pricing.