Application Of Backward Stochastic Differential Equation In Option Pricing

Since 1973,Black and Scholes of American financiers put forward the classical Black-Scholes option pricing formula,the application of option pricing model has been a hot issue in the field of finance.Although compared with overseas countries,China started late in options,in recent years,with the gradual improvement and development of financial market system,China's option market is becoming more and more active,and the scale and types of options are expanding.The related system of options is maturing,and the position of options in China's financial market is improving day by day.Increased number of investors in the options market as a result It is urgent to explore the option pricing model suitable for our country.Option pricing theory has been a hot issue at home and abroad.With its continuous development,option pricing theory has also spawned a new theory——inverted stochastic differential equation theory.Because of its excellent mathematical properties,inverted stochastic differential equations are widely used in the pricing of derivatives such as option futures.The reverse stochastic differential equation is applied to the option pricing model,and it is of great significance to further study the option market in China.The traditional option pricing model assumes that it is too idealized,but in the actual trading process,the dividend rate is often not negligible.Due to the payment of dividends,the price of the stock tends to decrease.This reduces the accuracy of the classical option pricing model.Therefore,this thesis studies the option pricing model of paying continuous dividend,and gives the method of solving the formula by using inverted random differential equation,which makes the model more practical and more in line with the characteristics of the option market in China.This thesis first introduces the current research situation at home and abroad,backward stochastic differential equations and options pricing theory,and lays a solid theoretical foundation for the following writing.Then the option pricing model for continuous dividend payment is established,and the option pricing formula for continuous dividend payment is solved by using the knowledge of inverted random differential equation,which improves the practicability of the model.to verify the pricing effect of the model,this thesis empirically analyzes the model based on the Shanghai 50 ETF option data.Considering that the volatility is not constant,the GARCH model will be used to fit the volatility to improve the option determination The prediction accuracy of the price model.Finally,by comparing the pricing effect of the classical option pricing model with the option pricing model that pays the continuous dividend,the theoretical model is closer to the reality.Empirical analysis results show that for both the pricing error of option pricing model which pays continuous dividend is smaller than that of classical option pricing model,whether for subscription option or put option.It shows that its pricing effect is better than the classical option pricing model and more suitable for China's option market.At the same time,according to the different periods of options,the fitting effect analysis is given,which can provide some theoretical reference for investors to carry out risk management.