Designing And Princing Of Options Related With Oil Bonds

This paper adopts non-parametric methods to overcome the defect of parametric model research, uses Kolmogorov equation and conjugate equation to obtain the relationship of volatility rate, drift rate and the interest rate density function of term structure of interest rate, and constructs the expressions of volatility rate and the interest rate density function by non-parameter kernel density estimation method, then gets the drift rate function of the term structure of interest rates. Putting such a new method into the pricing of options related with oil bond, at the same time, combining risk neutral probability and using binomial-tree numerical pricing method to calculate of the issue price of option related with oil bond.In order to better reflect the research value of the method, the paper considers the pricing options pricing related with oil bond whose rate obeys Vasicek term structure of interest rate model. Using delta-hedge to obtain the corresponding partial differential equation model under no-arbitrage market hypothesis, Finally obtaining the analytical solutions and issue price of options related with oil bonds based on Vasicek the term structure of interest rate model by changing the price units and partial differential model of zero coupon bonds. This paper also considers the pricing options pricing related with oil bond whose rate obeys CIR term structure of interest rate model, using delta-hedge to obtain the corresponding partial differential equation model under no-arbitrage market hypothesis. This paper adopts the Monte-Carlo simulation method to realize the numerical solution of the model.Finally contrasting options related with oil bonds based on above three different kinds of term structure of interest rate model, the paper can conclude:in the drift rate estimates:the drift by non-parametric methods estimated is the nonlinear function of the interest rate, and CIR model and Vasicek model both assume that drift is a linear function of interest rate; in volatility rate estimates, Vasicek model hypothesis that the volatility of stochastic process model is constant, CIR model hypothesis that the volatility of stochastic process model is the linear function of interest rate, and volatility by non-parametric methods estimated is the nonlinear function of interest rate. With interest rates of the CIR model and Vasicek model express mean reversion of interest rate, non-parameter rate model can also shows a weak mean reversion characteristics. In pricing:the price of options related with oil bonds based on non-parametric term structure of interest rate is the lowest, the price of options related with oil bonds based on Vasicek term structure of interest rate is the highest.