A Tractable Multi-Factor Dynamic Term-Structure Model for Risk Management

Abstract

We present an affine arbitrage-free dynamic term-structure model based on a representation of instantaneous forward rates as sum of exponentials. The model, which is Gaussian and belongs to the class of Heath-Jarrow-Morton-type models, is intuitively appealing as a suitable linear combination of the stochastic factors can be interpreted as stochastic evolution of stable principal components of the yield curve. Focusing on applications, we derive general principal components in such an affine-linear model, calibrate the model to government bond prices, and derive simple formulas to price caps and floors.

Keywords: Affine term-structure models, principal components, Heath-Jarrow-Morton, restricted exponential model, multi-factor Hull-White, G2

JEL Classification: E43, E47, G12, G13