A Family of term-structure models with stochastic volatility for use in dynamic financial analysis

In this paper we extend the class of multifactor term-structure models proposed by Cairns (2004) to incorporate a more explicit form of stochastic volatility. The models are built up within the framework proposed by Flesaker & Hughston (1996).

Our general aim is to work with models in which zero-coupon bond prices can be expressed in the form
[see paper for equation]
for some n-dimensional, stationary diffusion X(t) and for suitable deterministic functions A(u) and B(u). We prove that the models require a multivariate affine state-variable X(t) as developed previously by Duffie & Kan (1996). The remainder of the paper describes some numerical experiments for specific two and three-factor models which incorporate one stochastic volatility component.

The models have a close relationship with recently developed market models incorporating stochastic volatility. The new models can therefore be used to provide practitioners with a parsimonious benchmark against which more elaborate market models can be compared.

Keywords: term-structure model; multifactor; positive interest; stochastic volatility; time-homogeneous; log-normal; term-structure of volatility.