TITLE:
Interest Rate Models
AUTHORS:
Alex Paseka, Theodoro Koulis, Aerambamoorthy Thavaneswaran
KEYWORDS:
Affine Process; Dynamic Term Structure Models; Jump-Diffusions; Quadratic-Gaussian DTSMs
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.2 No.2,
May
23,
2012
ABSTRACT: 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.