Hongtao Yang

Numerical Pricing of Interest Rate Derivatives

Hongtao Yang
University of Nevada

In this talk, I shall present our recent work on numerical pricing of zero-coupon bonds and their options. The values of these financial securities crucially depend on the random fluctuations of short interest rates. Among various models of interest rates, we consider the time inhomogeneous affine models which are so-called arbitrage free models. Indeed, the time-dependent parameters of the models can be determined by using the current term structure of interest rates and other market information so that they can produce arbitrage free bond prices. In the first part of the talk, I shall consider the inverse problem for calibration of the extended CIR model. The constructive proof of the solution existence and uniqueness naturally leads to an efficient algorithm to compute the time-dependent parameters and bond prices numerically. In the second part of the talk, I shall consider a finite element method for American bond options. The option pricing problems are reformulated to a variational problem with a coercive bilinear form. Numerical examples will be presented to examine the proposed numerical methods and to compare the Hull-White model and the extended CIR model.