Study On Pricing Of Derivative Securities Under Stochastic Interest Rate Model

In financial mathematics, the pricing of interest rate derivative securities is an important and meaningful issues which is of both theoretical and practical value, in the fields of the study of pricing of Derivative Securities with interest rate being a constant or fixed un-random functions. scholars have made a lot of achievements, however, the research works in concern with the situation when the interest rate being stochastic are less, But the variants of price and interest rate which the value of derivative securities depended upon are always some stochastic process with uncertainted changing features. Theofore, the study of derivative securities pricing which based on the model of random interest rate meets the practical demond. This paper mainly studied the price fixing of derivative securities under the random interest rate model which applied stochastic differential equations on the basis of option pricing theory and the model of derivative securities pricing, several major findings are summarized as follows:(1) Based on analyzing the Vasicek stochastic interest model, we transform the long-run mean, fluctuation rate and restoration are constant into fixed functions about t, In this assumption, we build a new model, by means of solving partial differential equation based on the Extended Vasicek interest model. Furthermore, we give the bond-pricing formula of discounted and the bond-choose of discounted with a face time of T and pay one Yuan by using Ito Lemma and build the constitute of bond.(2) The pricing formula of European Call option and the put-Call party relation in a completed and continuation marketed model are gived, which the process of asset price is assumed to be Vasicek model with a fixed function about time. By using Ito formula Black-Schole's risk-neutral valuation principal.(3) Studied the European option of Pricing on maximum or minimum of risk assets in Vasicek model with a fixed function about time, and give a relationship of European Put options on maximum or minimum of n kinds of assets in stochastic Vasicek model. Which assets prices follow the lognormal distributions, that the process of interest rate follows Vasicek model with a fixed function, Using martingale and the theory of no-arbitrary.(4) Under a two factor Vasicek model of term structure of interest rates in which both the short and its short term mean are assumed to be stochastic, I give the pricing formula of bond option.