This paper nonparametrically estimates a continuous-time Markov model of term structure dynamics. Due to the quot;aliasing problemquot;, which tells us that the drift and diffusion of the short rate process are not identifiable given only discretely sampled data, previous authors have parameterized at least one of the drift and diffusion functions, leaving open the possibility of misspecification. This paper imposes no parametric restrictions on either the drift or the diffusion, instead deriving and estimating a family of approximations to the true drift and diffusion functions. These approximations are identifiable using only discretely observed data, and for some common parametric models, we find that the approximations are almost indistinguishable from the true drift and diffusion when the sampling frequency is monthly or greater. Estimating the model using daily data on the 3 month Treasury Bill rate over the period January 1965 - July 1995, we find that, while the estimated diffusion is similar to the (parametric) function estimated by Chan, Karolyi, Longstaff and Sanders (1992), there is evidence of substantial nonlinearity in the drift, showing sharply increasing mean reversion as the short rate moves further from its long run mean. Knowing the process governing short term interest rate movements is not enough by itself to price interest rate derivative securities. We also need to know the market price of interest rate risk, the excess return required for an investor to bear a unit amount of additional risk. Previous research has typically assumed this to be identically zero. We explicitly estimate the functional relationship between the market price of interest rate risk and the level of interest rates, using daily excess returns on 6 month vs. 3 month Treasury Bills over the period January 1965 - July 1995, and combine this with the estimated short rate model to price interest rate dependent securities. Incorporating our estimates for the market price of interest rate risk changes the pricing results substantially.