债券定价及利率风险的市场价格的重构方法

Method of the bond pricing and the market price of the interest rate risk

假设利率变化的模型是由随机微分方程给出,则可以用推导Black-Scholes方程的方法来推出债券价格满足的偏微分方程,得到一个抛物型的偏微分方程.但是,在债券定价的方程中隐含有一个参数λ称为利率风险的市场价格.所谓债券定价的反问题,就是由不同到期时间的债券的现在价格来得到利率风险的市场价格.对随机利率模型下债券定价的正问题先给予介绍和差分数值求解方法,并介绍了反问题,且对反问题给出了数值方法.

Assume that the interest rate fluctuating model is given by the stochastic differential equations,then we can use the derivation for Black-Scholes equation to deduce a parabolic partial differential equation which satisfies the bond prices.But the bond pricing equations imply a parameter which is called the market price of the interest rate risk.The so-called inverse problem of bond pricing,that is,to get the marker price of the interest rate risk with current bond prices of different maturates.Stochastic interest rate model for bond pricing and the difference numerical method are introduced,and the numerical method for the inverse problem is also proposed.