Research On Least Squares Monte Carlo American Options Pricing Based On GPU

Options are financial derivatives as trading contracts.Options pricing plays a vital role in financial product innovation,hedging,and risk management.Most of the options currently traded in the financial market are American options.American options can be executed early,closed solutions cannot be obtained,which makes the pricing of American options more difficult.The numerical methods solved are binary tree,finite difference,Monte Carlo method,and so on.The binary tree method can also calculate one-dimensional assets.However,when calculating the assets used for high-dimensional targets,it encounters a dimensional disaster.The finite difference method performs the transformation from differential equation to difference equation.Iterative method can be used to solve the difference equation,which avoids the difficulty of directly solving the differential equation.However,when solving the high dimensional problem,the"dimensional disaster" will also occur and it is difficult to overcome.Monte Carlo method has strong versatility in the field of option pricing,which can solve high-dimensional problems and parallelization is easy to implement.Therefore,the classic method of American option pricing is Least Squares Monte Carlo(LSM).With the number of simulation paths and time intervals increases,the calculation of options pricing is getting bigger and bigger,and it is more and more difficult to price options on traditional CPU platforms.In recent years,GPU(Graphic Processing Unit)general-purpose computing as an emerging high-performance computing method provides a solution for option pricing calculation.Therefore,this paper uses the least squares Monte Carlo method to calculate the pricing of one-dimensional and four-dimensional American options based on GPU.The specific work is as follows:(1)In view of the long time-consuming problem of American option pricing,based on the parallel analysis of LSM algorithm,a GPU-based LSM algorithm is proposed,and the parallel computing process is realized by CUDA.Further communication,memory access and instruction stream optimization for the algorithm,and using the antithetic variates to improve the simulation efficiency of one-dimensional American options;(2)Propose the four-dimensional American option pricing LSM algorithm based on GPU,and the CUDA implementation process of the algorithm is given.The performance optimization strategies are proposed,such as communication,load balancing and data prefetching.In the case of maintaining pricing accuracy,the antithetic variates is used to reduce the variance and improve the pricing efficiency of the four-dimensional American option;(3)Compare and analyze the one-dimensional and four-dimensional American options based on GPU and CPU.On the GPU heterogeneous platform,test the sample path of the generated asset price,the optimal execution time of each sample path,and the pricing of each sample path are compared with the path number in the American option pricing process.Experiments with changes in time intervals,comparisons with papers[41]and[43],and antithetic variates were also tested;(4)According to theoretical research and test analysis,the experimental results show that the acceleration ratio of one-dimensional American option pricing can be up to 20.275,and the four-dimensional American option pricing can be optimized up to 47.538,which accelerates the entire pricing process.