Barrier Option Pricing Under Stochastic Volatility And Stochastic Interest Rate Model

Option is one of the important members of financial derivatives.In the modern financial market,it is a financial instrument derived based on futures.It is the core tool for financial investors to realize investment and risk control.In the past three or four In the past ten years,the rapid development of financial derivatives at home and abroad has become one of the most brilliant developments in the financial market.Therefore,how to reasonably price options is a hot research topic in the financial and academic circles.In recent years,With the continuous development of the financial market,many new types of exotic options have emerged in the financial market.Among them,barrier options are one of the most representative weak path-dependent options.The expiration date of barrier options does not only depend on expiration The daily option price is also related to whether the original asset price can reach a certain predetermined barrier value in a certain period of time.Generally speaking,barrier option is a cheaper option than standard option Therefore,barrier options are favored by financial investors and financial institutions in the financial investment market.For financial institutions,under the premise of effective risk control,how to maximize investment benefits and minimize investment risks is one of the important development concepts of financial institutions.Therefore,how to accurately consider a variety of factors that affect option pricing Factors are one of the most important links.Therefore,under the premise of considering the reality,this article adopts the market model of option pricing is a random volatility and random interest rate model that combines multiple influencing factors in the market.Generally speaking,in actual finance In the market trading rules,the trading time of financial derivatives is often discrete.Therefore,the study of barrier option pricing in discrete time is closer to the reality and has more practical significance.Due to the limitations of the classic Black-Scholes model in describing the price movement of basic assets in the complex and changeable financial market,in order to better get close to the changes in the actual market,scientific researchers in the financial sector continue to improve Black-Scholes.Scholes model,and introduces different types of option models.For example,CIR stochastic interest rate model,Heston stochastic volatility model,etc.Therefore,this article comprehensively considers the impact of volatility and interest rates on option pricing,and the underlying asset price is based on stochastic volatility And the stochastic interest rate model(denoted as the SVSI model)studied the pricing problems of European discrete barrier options and Asian discrete barrier options,and applied relevant stochastic analysis techniques and mathematical methods such as Fourier inverse transformation,Feynman-Kac theorem,PDF equation and Girsanov measure transformation and mathematical induction methods,deduced the pricing formulas of European discrete barrier options and Asian discrete barrier options under stochastic volatility and stochastic interest rate models.Through numerical analysis and other methods,the stochastic volatility and stochastic interest rate models are analyzed.Take the different values ??of related parameters as an example to study the price changes of European discrete barrier options and Asian barrier options.Therefore,in the financial market,financial institutions and financial investors should comprehensively consider various factors in the pricing of barrier options.Under the stochastic volatility and stochastic interest rate models,price European barrier options and Asian discrete barrier options,Investors can obtain option prices that are more in line with their options,and provide references for financial investors in investment transactions in the financial market,so that barrier options can play an active role in the financial market.In addition,this article also addresses barrier options pricing issues.The research provided a new way of thinking.