Author(s)

Alex Paseka, Theodoro Koulis, Aerambamoorthy Thavaneswaran

Department of Accounting and Finance, University of Manitoba, Winnipeg, Canada; Department of Statistics, University of Manitoba, Winnipeg, Canada.

In this paper, we review recent developments in modeling term structures of market yields on default-free bonds. Our discussion is restricted to continuous-time dynamic term structure models (DTSMs). We derive joint conditional moment generating functions (CMGFs) of state variables for DTSMs in which state variables follow multivariate affine diffusions and jump-diffusion processes with random intensity. As an illustration of the pricing methods, we provide special cases of the general formulations as examples. The examples span a wide cross-section of models from early one-factor models of Vasicek to more recent interest rate models with stochastic volatility, random intensity jump-diffusions and quadratic-Gaussian DTSMs. We also derive the European call option price on a zero-coupon bond for linear quadratic term structure models.

Affine Process; Dynamic Term Structure Models; Jump-Diffusions; Quadratic-Gaussian DTSMs

A. Paseka, T. Koulis and A. Thavaneswaran, "Interest Rate Models," Journal of Mathematical Finance, Vol. 2 No. 2, 2012, pp. 141-158. doi: 10.4236/jmf.2012.22016.