Research On Several Models And Methods Of Option Pricing

Option pricing is one of the front-burner topics in financial mathematics.An option is a right that investors can buy or sell underlying assets at a set price within a specified time.Black-Scholes model is the most traditional pricing model.However,there are some shortcomings in this model.Firstly,it cannot describe the characteristics of changes of underlying asset price.Second,it cannot describe the changes of interest rate over time.As a result,it is of great significance to create innovation pricing models which is more consistent with the changes of underlying asset price in the monetary marketplace.According to the theory of option pricing,in this thesis we mainly study three pricing models.Firstly,we establish a pricing model of look-back option driven by the sub-diffusive process,and integrate periods of constant values of underlying assets into the pricing model.We obtain the partial differential equations satisfied by look-back option by using Delta hedging technique,and give the numerical simulation results of the model by using the finite difference method.Secondly,we construct the pricing model of two-asset geometric Asian rainbow option in sub-diffusive process.By using partial differential equation method and variable transformation to deduce the pricing formula for option and give the related numerical calculation.Finally,we establish the European option pricing model with Merton stochastic interest rate.By incorporating the sub-mixed fractional Brownian motion and stochastic interest rate into the option pricing model at the same time,we obtain the pricing formulas for European option and discuss the problem of the implied volatility.Moreover,we give numerical results and compare with other classical pricing models.