Numerical Algorithm Of Option Pricing Based On Deep Learning

With the development of the trading market,standard European and American options can not meet the needs of customers,so exotic options emerge as the times require.Their structure and trading methods are more flexible than ordinary options.With the increase of exotic options,it is necessary to study them.This paper selects two typical options——basket options and Asian options to do research.On the other hand,in recent years,deep learning has developed rapidly,and has been applied in various fields,whether in engineering or scientific research,and has made great progress.At the same time,many foreign scholars have begun to study how to combine deep learning with solving equations,and achieved fruitful results.This paper mainly includes the following two parts:the first part describes that the stochastic differential equation satisfied by the price of basket options is high-dimensional,because the "Curse of dimensionality" is difficult to be solved by analytical methods,so we use the deep learning numerical algorithm to solve this problem,and use the Monte Carlo algorithm to verify the accuracy and speed of the algorithm.Finally,the control variable method was used to carry out many experiments to explore the influence of experimental parameters;The second part mainly focuses on the Asian option,because of its path dependence,it is difficult to find its analytical solution,especially the arithmetic average Asian option.We select three kinds of Asian option models(one dimension arithmetic average,high dimension arithmetic average,geometric average)to explore a general algorithm for Asian options,and verify its accuracy by comparing with other algorithms.