A numerical solution of the pricing model of Asian options under sub-fractional jump-diffusion process. (Chinese. English summary) Zbl 1449.65183
Summary: Under the assumption of the sub-fractional Ho-Lee stochastic interest rate model, this research firstly uses the delta hedging principle and establishes the partial differential equation of geometric average Asian options under the sub-fractional jump-diffusion process with transaction costs and dividends. Secondly, the pricing model is simplified to the Cauchy problem by using the variable substitution. Finally, a numerical solution of the pricing model is given by using the finite difference method and the composite trapezoid method. An example is also given to verify the effectiveness of the algorithm design.
MSC:
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
91G20 | Derivative securities (option pricing, hedging, etc.) |
91G30 | Interest rates, asset pricing, etc. (stochastic models) |
35R11 | Fractional partial differential equations |
26A33 | Fractional derivatives and integrals |
91G60 | Numerical methods (including Monte Carlo methods) |
60J65 | Brownian motion |
91B24 | Microeconomic theory (price theory and economic markets) |