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.
Highlights
In this review, we summarize available continuous time technology for pricing default-free term structures
Our discussion is restricted to continuous-time dynamic term structure models (DTSMs)
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
Summary
We summarize available continuous time technology for pricing default-free term structures. The most redeeming features of this class of models are the availability of closed form solutions for derivatives on the short rate and the ability of models to reproduce a variety of term structure patterns. We consider a recent extension of a class of Linear-Quadratic term structure models (LQTSMs) to a class of jump-diffusion TSMs in which short rate jump intensity follows its own stochastic process (see [36,37,38] for details). We show how this model class is designed to have a closed form conditional moment generating function and bond prices. We derive the price of a European call option using a generalized transform
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