Estimation of risk-neutral processes in single-factor jump-diffusion interest rate models

The estimation of the market price of risk is an open question in the jump-diffusion term structure literature when a closed-form solution is not known. Furthermore, the estimation of the physical drift has a high risk of misspecification. In this paper, we obtain some results that relate the risk-neutral drift and the risk-neutral jump intensity of interest rates with the prices and yields of zero-coupon bonds. These results open a way to estimate the drift and jump intensity of the risk-neutral interest rates directly from data in the markets. These two functions are unobservable but their estimations provide an original procedure for solving the pricing problem. Moreover, this new approach avoids the estimation of the physical drift as well as the market prices of risk. An application to US Treasury Bill data is illustrated.