The Application Of Importance Sampling In Barrier Option Pricing With Stochastic Interest Rate

Option pricing is an important issue of both theoretical and practical value in the field of financial mathematies.About the research on path-dependent option,domestic and foreign scholars have done a lot of research work under the condition that the risk-free interest rate or interest rate is a deterministic function of time,for example,Giray Okten and Emmanuei Salta published a barrier-free option pricing under risk-free rate in 2008_But when the interest rate is a random variable,the current research results are rare.So this paper discusses the problem of variance reduction of barrier option pricing based on the stochastic interest rate model,including the following aspects:Monte Carlo options pricing theory,variance reduction method,Monte Carlo method pricing based orn Vasicek model and Monte Carlo method pricing based on CIR model.This article discusses the pricing of option that is based on the stock as the underlying asset,the behavior of the stock price is described in detail.And Monte Carlo pricing equation that meets the barrier option is deduced by conditional expectation Monte Carlo simulation method by constructing a portfolio of derivative securities and underlying stocks under a non-arbitrage framework and two models of stochastic interest rates.Tben the sample of importance will be used to reduce the variance.Finally,bring the data for simulation analysis.