Hongtao Yang
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Numerical Pricing of Interest Rate Derivatives

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Hongtao Yang

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University of Nevada
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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.