The Term Structure of Interest Rates Under Heath–Jarrow–Morton Models with Fast Mean-Reverting Stochastic Volatility

Abstract

This paper is a study of the term structure of interest rates based on the Heath–Jarrow–Morton (HJM) models with Hull–White volatility function. Under fast mean-reverting stochastic volatility, we obtain an analytic formula for an approximate bond price with estimated error using a Markovian transform method combined with a singular perturbation method. The stochastic volatility correction effect against time-to-maturity is revealed so that it can capture more of the complexities of the interest rate term structure.