A Stochastic Monetary Policy Interest Rate Model

Abstract

A new stochastic monetary policy interest rate term structure model is introduced within an arbitrage-free framework. The 3-month spot LIBOR rate is taken as modelling primitive and the model is constructed with local volatility, asymmetric jumps, stochastic volatility regimes and stochastic drift regimes. This can be done in an arbitrage-free framework as the chosen modelling primitive is not an asset price process and therefore its drift is not constrained by the no-arbitrage condition. The model is able to achieve a persistent smile structure across maturities with a nearly time homogeneous parameterisation and explain steep, flat and inverted yield curves, consistently with historical data. It is shown that the drift process, which is made correlated to the underlying LIBOR rate, is the main driver for long time horizons, whilst jumps are predominant at short maturities and stochastic volatility has the greatest impact at medium maturities. As a consequence, the drift regime process provides a powerful tool for the calibration to the historical correlation structure and the long dated volatility smile. The model is solved by means of operator methods and continuous-time lattices, which rely on fast and robust numerical linear algebra routines. Finally, an application to the pricing of callable swaps and callable CMS spread range accruals is presented and it is shown that this modelling framework allows one to incorporate economically meaningful views on central banks’ monetary policies and, at the same time, provides a consistent arbitrage-free context suitable for the pricing and risk management of interest rate derivative contracts.