A bivariate Hawkes process for interest rate modeling

This paper proposes a continuous time model for interest rates, based on a bivariate mutually exciting point process. The two components of this process represent the global supply and demand for fixed income instruments. In this framework, closed form expressions are obtained for the first moments of the short term rate and for bonds, under an equivalent affine risk neutral measure. European derivatives are priced under a forward measure and a numerical algorithm is proposed to evaluate caplets and floorlets. The model is fitted to the time series of one year swap rates, from 2004 to 2014. From observation of yield curves over the same period, we filter the evolution of risk premiums of supply and demand processes. Finally, we analyze the sensitivity of implied volatilities of caplets to parameters defining thelevel of mutual-excitation.