Our purpose of this paper is to show how the asymptotic method developed in Cotton et al. [2] and Fouque et al. [7] in the context of the Black-Scholes theory is applied to interest rates. We do this by considering simple models of short rates (such as the Vasicek model) and computing corrections that come from a fast mean-reverting stochastic volatility given by a nonnegative function of a fractional Ornstein-Uhlenbeck (fOU) process. Here, fOU process is driven by a fractional Brownian motion (fBm) with arbitrary Hurst parameter  What is important for the asymptotic results we present is that fOU process is characterized by a, the rate of mean-reversion, and has a unique invariant probability distribution  that is, the normal distribution with mean mand variance

The asymptotic approximations we present are in the limit  with  fixed, which we refer to as fast mean-reversion. We assume that volatility shocks and interest rate shocks are independent.

Then we obtain the corrected price for zero-coupon bond so that it is expanded around the usual Vasicek one-factor bond pricing function with the averaged parameters related to stochastic volatility model parameters.

Since for  fractional Brownian motion is neither a Markov process, nor a semimartingale, usual stochastic calculus cannot be applied to our model. Therefore, instead of the probabilistic approaches such as the use of conditional expectation, standard Ito formula and the Feynman-Kac representation, our research is made by the fractional integration theory which is due to Hu [10] and partial differential equation approach.

More precisely, we derive bond pricing partial differential equation by fractional Ito formula, introduce fast-scale to model fast mean-reversion in stochastic volatility, and hence obtain the expression for corrected price for zero-coupon bond so that it is characterized by the averaged parameters which are computed as the averaged values with respect to the invariant probability distribution of the fOU process.

Here, asymptotics in the fast-scale is made by singular perturbation expansion, analogous to these in Fouque et al. [5-7] and Narita [14-16]. This again leads to a leading order term which is the usual Vasicek one-factor bond pricing function with the corrected mean level related to fOU process. Our theorem is an extension of the results in Cotton et al. [2] and Fouque et al. [7] to a fractional Vasicek model in the case that fluctuations in price and volatility have zero correlation.

interest rate, bond price, Vasicek model, stochastic volatility, fractionalBrownian motion, fractional Ornstein-Uhlenbeck process, singular perturbation.