Research On Term Structure Of Interest Rate Under Jump Diffusion Model And Its Applications In Risk Management

The term structure of interest rate is a basic and important research in today's financial risk management.At the same time,interest rate is an effective link between macro economy and micro economy,it is also one of the basis for the government to regulate and manage the economy.Interest rate will change due to the interference of external factors,so it is particularly important to study the related problems of the term structure of interest rate.There are many kinds of term structure models of interest rate,among which Dothan model proposed in 1978 and HJM model proposed by heath,Jarrow and Morton in 1992 are the most representative.Dothan model considers the non negativity of interest rate,and assumes that volatility and drift terms are constant,which is more convenient to deal with.HJM model is an improvement of Ho Lee model.The principle is to simulate the forward interest rate.In 1976,Merton proposed the jump diffusion model,which can better explain the impact of emergencies on interest rate,exchange rate,stock price and other factors.This paper mainly studies the jump diffusion model of interest rate term structure.This paper makes a comprehensive study on Dothan model and single factor HJM model under jump diffusion model respectively.Under the condition of finite jump point in finite time,by using the method of risk neutral measure transformation,we get the pricing of European call option with immediate interest rate and post LIBOR under jump diffusion model.At the same time,under the risk neutral measure,we get the pricing of European call option with immediate interest rate under jump diffusion model.Finally,use the research results to make decisions,carry out risk management on the interest rate risk with jump,achieve the effective transfer of risk and conducive to investors' investment.