Multilevel Monte Carlo Method Of Financial Option Pricing

When the market is not completely effective,the Black-Scholes model with constant volatility can no longer accurately depict the real-world financial market.This leads to the stochastic volatility model,in which the Heston model is a classical and commonly used stochastic volatility model.Under this model,We are studied the European option,the Asian option and the lookback option.Firstly,this paper presents the discrete format and Multilevel Monte Carlo algorithm of the Heston model.Secondly,the computational complexity of the model is analyzed theoretically.Finally,the simulation is carried out with Matlab program.The simulation results are applied to the European,the Asian and the lookback option.The numerical results test the efficiency of the Multilevel Monte Carlo method compared with the Monte Carlo method.Moreover,this paper studies the stochastic optimal control problem of Black-Scholes model.We give its optimality condition,Milstein discrete scheme,simple theoretical analysis of Monte Carlo method and Multilevel Monte Carlo method,and a Multilevel Monte Carlo algorithm for option pricing.Numerical examples show that the larger the standard deviation is in the range of variance,the greater the deviation the calculated approximate solution and the accurate solution is.Multilevel Monte Carlo method improves the shortcoming and thus more accurately simulates the option price in the option pricing problem.