On the calibration of the Cheyette interest rate model

Abstract

We investigate the robustness of existing methods to calibrate the Cheyette interest rate model to at-the-money swaption, caps and floors. Existing algorithms may fail, because they suffer from numerical instability of derivatives. Therefore, we apply derivative-free techniques and find that they stabilize the calibration. Furthermore, we identify auspicious volatility parametrizations determining the Cheyette model. In combination with the established calibration techniques the results imply an accurate market reproduction and stay robust against changes in the initial values. In contrast to existing approaches that use approximations, we apply exact semi-close-form pricing formulas.