American Option Studies Via Quasi-Monte Carlo And Generalized IPA Approach

Option is one of the most important financial derivative instruments,and American option pricing and sensitivity analysis is a very crucial issue encountered in today's financial markets.To make options function properly and efficiently,fair pricing is of vital importance.For some European-style options,current studies have already given a closed solution,that is,it can be deduced from the formula.Given any independent variable,the dependent variable can be obtained.For example,the well-known BlackScholes model provides a closed-form solution for the value of some European call options and put options.However,due to the early-execution features of American options,it is often only possible to use numerical solutions,that is,to approximate solutions using numerical methods.In addition,when the dimension of the problem is relatively large,partial differential equations and numerical integration become difficult to handle,and it is difficult to use traditional methods for accurate evaluation.In these cases,the Monte Carlo method usually gives better results because it has proved to be a well-appropriate computing tool.Therefore,in the past decade,option researchers have proposed many methods based on Monte Carlo simulation to solve the problem of pricing and sensitivity of American derivatives.For example,the finite difference method and the least squares fitting method.However,using the Monte Carlo method has a significant drawback,that is,the volatility of the simulation results is relatively large,especially under the influence of the few simulation paths plus multi-base assets,and the inaccuracy of this result is quite serious.In order to improve the accuracy of the simulation results,the Monte Carlo simulation path is often increased,and doing so will greatly increase the calculation time.Therefore,this thesis will try to use Quasi-Monte Carlo,which uses a low-bias sequence instead of a pseudo-random sequence as a basic sample of random numbers.In addition,for the price and sensitivity calculation of American options,we try to implement the generalized IPA method.The framework of this paper is as follows: First,we will introduce the American option and its pricing and sensitivity calculation methods.Second,we will use the general IPA method to calculate the price and sensitivity of the American option,and then compare the performance of the generalized IPA method,the least squares,and the CRR method based on the calculated standard error of the option value.Finally,we use Monte Carlo and Quasi-Monte Carlo methods(Halton and Solbol)to calculate the value of American options with multiple fundamental assets.The results show that the Monte Carlo method is superior to traditional CRR method,and quasi-Monte-Carlo simulation method,especially Sobol,is significantly better than the Monte Carlo method in terms of variance reduction,and the volatility of the option price calculated by the generalized IPA method is relatively small too.