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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](/sites/default/files/styles/x_small_square_1_1/public/image/2024-02/Dr.%20Alexandre%20Antonov.jpeg?h=55541bb6&itok=f-aF1kGu)
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.