Wishart Process And Affine Interest Rate Model

The various kinds of affine interest rate model play very important roles in inter-est rate market modeling. The classic one-dimension or bi-dimension affine models, however, see their lack of capacity to explain miscellaneous types of changes of fi-nancial products prices on the market. The subject of this paper is Wishart process volatility affine interest rate model, which actually can be regarded as a generaliza-tion of Hcston interest rate model to multi-dimension. Wishart process is a class of stochastic process taking value in the set of symmetric positive-definite matrix, and the Wishart process stochastic volatility affine interest rate value assumes that the dynamic of interest rate is an affine function of several state variables whose covariance matrix is an affine function of a Wishart process. This paper focuses on the valuation methods of financial instruments such as zero-coupon bond and caplet under the Wishart process interest rate model. We get the closed-form valuation formulas for some special examples. In general case, we need numerical methods such as FFT algorithm. This thesis, through an example, also presents the advance that this high-dimensional model has made on explaining the price fluctuation of these instruments. At last, the author also presents some preliminary discussions on the issue of the calibration problem of this model.