General short-rate analytics

Alexandre Antonov and Michael Spector present an analytical approximation of zero-coupon bonds and swaption prices for general short-rate models. The approximation is based on regular and singular expansions with respect to low volatility and contains a low-dimensional integration. The model in hand assumes the short rate is an arbitrary function of a multi-dimensional Gaussian underlying process. The high approximation accuracy is confirmed by numerical experiments

Short-rate models underlie the first steps of quantitative finance development. The main feature of such models consists of postulating the short-rate process. Vasicek (1977) and Hull & White (1990) pioneered a Gaussian short-rate model still popular among practitioners due to its analytical tractability and transparency. Black & Karasinski (1991) have proposed a lognormal short-rate model. Both models share the same Gaussian mean-reverting process but with different interpretations in terms of