In the first passage structural approach, default occurs when the underlying reaches a default barrier. In the classical Black-Cox model the underlying follows a geometric Brownian motion with constant volatility. Probability distributions of first passage times are used to compute default probabilities. One of the undesirable features of this model is that the yield spreads at short maturities is almost zero which is in contradiction with observed yield spreads. We propose here to look at the effect of stochastic volatility on the yield spreads. We show that volatility time scale is an essential concept in understanding this effect. Perturbation methods are used to approximate defaultable bond prices for instance. From the probabilistic point of view we propose approximations to the probability distributions of hitting times of "Brownian motion with stochastic diffusion".