| Based on the BSM pricing formula,this paper uses Monte Carlo simulation method and quantum Monte Carlo simulation method to solve the European option pricing problem,and discusses the advantages and disadvantages of the three methods.It can be divided into the following parts:According to the European call option and put option formula of BSM option pricing model,the properties and the use conditions of the pricing model,the bullish and bearish prices of example options are solved by BSM pricing model.BSM pricing model is the theoretical basis of European option pricing.Based on concrete examples,this paper analyzes that the pricing factors of classical BSM option pricing model are affected by many aspects.For example,the price of the subject matter（S0）,the strike price（K）,the volatility of the subject matter price（σ）,the remaining time to maturity（T）,and the risk-free interest rate（r）can all constitute the options as influencing factors.The experimental results obtained are analyzed with the theory.In order to avoid the problems of the BSM pricing model in terms of option pricing dimension problem and convergence problem,we can perform multiple operations through the Monte Carlo method in mathematical statistics to solve the average price and expected value of options.The Monte Carlo method（MC）method is one of the main methods of simulating option pricing,but this method requires a large number of simulations to guarantee the huge and expensive accuracy of the amount of calculation.Monte Carlo simulation to European option pricing is also based on the BSM pricing model,using the Monte Carlo simulation method to solve European call options in specific examples,and obtain the estimated European option price and the underlying asset path simulation diagram.The relationship between the number of simulations,the number of discretization points and the accuracy of Monte Carlo’s algorithm is confirmed,and the time spent on different simulation times is obtained,and the experimental results obtained are analyzed with theory.By leveraging the laws of quantum mechanics,quantum computers can provide new ways to solve computationally intensive problems.To solve the above computational problem,the quantum Monte Carlo（QMC）model was established and applied to related systems such as European call options.This paper uses MC and QM methods to simulate European call options.It shows how to prepare quantum states,prepare related probability distributions in the process of quantum state superposition,how to use quantum gates and quantum circuits to build quantum circuits,and realize payment functions through quantum circuits,and finally make quantum states collapse through quantum measurements to obtain the price of financial derivatives.Through specific examples,this paper shows the algorithm process of quantum Monte Carlo simulation for option pricing,how to apply the amplitude estimation algorithm to achieve the number of steps required to achieve the second quantum acceleration,in particular,the maximum likelihood estimation quantum amplitude estimation method is introduced,and the probability distribution plot and return function plot of the asset price on the expiration date are obtained.The analysis confirms the relationship between the number and accuracy of qubits,as well as with time. |
