2025/06/30 by Alexander Gairat, Gairat, Alexander, Vyacheslav Gorovoy +3 · 1 voice
Economics, Econometrics and Finance · #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #q-fin.MF #q-fin.PR
paper · pdf · doi:10.48550/arxiv.2506.23876
arxiv published 2025/06/30 · arxiv updated 2026/03/30
This paper addresses the approximation of the local volatility function in the Cheyette interest rate model. Its main contribution is an explicit analytical formula for approximating local volatility, derived by extending the classical Dupire framework to interest rate models. In particular, an implicit Dupire-like expression for local volatility is first derived for options written on the short rate. This expression is then approximated using a combination of perturbation methods and probabilistic techniques, resulting in a formula expressed in terms of time and strike derivatives of the Bachelier implied variance. The final formula naturally extends to multi-factor Cheyette models and provides a practical tool for model calibration.