Robust Log-normal Stochastic Volatility for Interest Rate Dynamics

Abstract

We introduce the log-normal stochastic volatility (SV) model for the dynamics of a short interest rate in the Cheyette model. We assume non-zero correlation between the dynamics of the short rate and the log-normal SV driver for modelling positive implied volatility skews observed in fixed-income derivatives. We show that our model is robust because the short rate process does not explode in finite time, in contrast to models which mix local rate dynamics with zero-correlated volatility dynamics. We obtain closed-form analytical solution for valuation of swaptions and for model calibration to market data. We show that our model is able both to fit accurately market implied volatilities and to be consistent with historical evolution of rates and volatilities.

Keywords: Interest rate volatility, log-normal stochastic volatility, Cheyette model

JEL Classification: G13, C63