The Formulas Of Interest Rate Derivatives Price Of Vasicek Model

In financial markets, interest rate derivatives attract more and more investors because of its low risk characteristics. Traditionally, the mainly method of interest rate derivatives pricing was using the martingale measure transformation, the key feature of this approach was that through appropriate measure transform, the draft rate changed into risk-free interest rate. However, this is not the only way to change the draft rate. In fact, the draft rate can be changed by adding a feedback control in the initial diffusion process, but keeping the same measure. Based on the traditional martingale method we present a stochastic control approach to price interest rate derivatives.Based on the research background and significance, research status, the basic concepts and theories, we introduce the basic idea of stochastic control method applied to bond pricing: apply a convex function of price to obtain a partial differential equation from the term structure equation, by determining the associated stochastic control problems and solving the corresponding HJB equation to get the optimal solution, then obtain the price formula of bonds. Then consider the special Vasicek interest rate model, with stochastic control approach we derive the explicit expressions of bond prices, which proved to be the same with the traditional methods of martingale.Next we extend the approach of stochastic control to forward measure and apply to the option pricing. At first, we derive that pricing with the forward measure can be equivalent to a pricing approach under the standard martingale measure. We finally got the explicit expression of bond options by the equivalence, which can be transformed into five simple linear integral, which have a great convenience in terms of calculation. We can also extend the stochastic control method further to an interest rate swap option, then we will get a system of methods of interest rate derivatives pricing.Although the interest rate derivatives of this paper is based on Vasicek model, but various popular models are amenable to this setting. The equivalence of calculate prices either on the basis of a traditional change of measure or by solving an optimal stochastic control problem, and the approach to price forward prices by forward measures, which have a great reference value on interest rate derivatives pricing for the term structure and other financial derivatives pricing.