Time Deformation and the Yield Curve

This paper considers how trading activity at one maturity of the yield curve a¤ects and is a¤ected by trading at other maturities. We approach the modelling of bond prices from a stochastic volatility perspective based on time deformation. We put forward a new, continuous time, multivariate time deformation model which is coherent with the market microstructure theory of price discovery and captures information ‡ow in the market. We model the stochastic volatility process by estimating the instantaneous volatility as a function of the price intensity in the spirit of Cho and Frees (1988) and Gerhard and Hautsch (2002). The point process model, a Hawkes model, that we use to model the price intensity allows for both the self and cross excitation e¤ects of trading at di¤erent maturities. Univariate and multivariate models are estimated using transaction level data from BrokerTec, a highly liquid and widely traded electronic platform for US securities. We …nd that the integrated price intensity is statistically supported as an appropriate directing process in the US bond market suggesting that private information is revealed indirectly through trades in the presence of information asymmetry and heterogeneous agents. We also …nd that the individual yields on US treasury notes and bonds appear to be driven by di¤erent ‘market clocks’ as suggested perhaps by the market segmentation theory of the term structure. These separate market time scales are then related to each other through a multivariate Hawkes model which e¤ectively coordinates activity along the yield curve. We also show that bond returns standardized by the instantaneous volatility estimated from our Hawkes model are Gaussian which is consistent with the theory of time deformation for security prices quite generally. JEL: C16, E43, F3, G1, G12