Analytical Approximations for Short Rate Models
In this article, we present the 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 the small 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.
We have treated two special classes of the model. The first one is a Generalized multi-factor Black-Karasinski (BK) model. The second one is a new Bounded short rate model where the rates evolve between certain user-defined limits. This model is particularly attractive for scenario generation and, due to the proposed swaption approximation, can be easily calibrated to the implied market.
Authors: Alexandre Antonov, PhD and Michael Spector, PhD
In this article, we present the 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 the small 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.
We have treated two special classes of the model. The first one is a Generalized multi-factor Black-Karasinski (BK) model. The second one is a new Bounded short rate model where the rates evolve between certain user-defined limits. This model is particularly attractive for scenario generation and, due to the proposed swaption approximation, can be easily calibrated to the implied market.
Authors: Alexandre Antonov, PhD and Michael Spector, PhD
Authors
Dr. Alexandre Antonov
Dr. Antonov received his PhD degree from the Landau Institute for Theoretical Physics in 1997 and joined Numerix in 1998, where he currently works as a Senior Vice President of Quantitative Research. His activity is concentrated on modeling and numerical methods for interest rates, cross currency, hybrid, credit and CVA. Dr. Antonov is a published author for multiple publications in mathematical finance, including RISK magazine and a frequent speaker at financial conferences.
