The Numerical Solution Of Heston Model And Its Greeks

This thesis mainly introduces calculation method of the Heston model and its Greek.Heston model is a stochastic volatility model which is developed by Heston in 1993.It is developed from the Black-Scholes model and let the unchanged volatility of Black-Scholes model be stochastic.Heston model now has wide use in stock option pricing.When Heston model is used in European option pricing,Heston gives a closed-form solution.We can use the closed-form solution to calculate its Greek.The closed-form solution of the Greek and European option price have similar function.Their closed solutions are mainly composed of a complex integral.The integral is difficult to calculate the solution directly.This thesis analyses this integral and adoptes different methods to calculate this integral,like trapezoidal integral method,Monte Carlo method,Quasi Monte Carlo method.When calculate Heston model we also use itself stochastic differential equation to do the simulation with Monte Carlo method.Because of the differential nature of the Greek itself,we also use the finite difference method when calculating Greek.Finally,we compare the different results in deviation,variance,and the time using to calculation.We find that the most simple trapezoidal integral method and Quasi Monte Carlo method are better than others.They achieve more accurate result.Because of the smoothness of European option price,the results of using finite difference method to do the calculation are very accurate when calculating the Greek.So we don't have to calculate its closed-form solution when calculating the Greek.Directly using the finite difference method is also a good choice.