Extracting Expectations in Affine Term Structure Models

In this paper, we study the problem of implementation of Ross (2015) Recovery theorem to disentangle the pricing kernel and physical probabilities from observed bond yields within discrete time affine term structure models. As a remedy to the problem of obtaining Arrow-Debreu prices of state transitions, we propose Markov chain approximation to autoregressive processes. Our work suggests that affine setting offers rich structure that enables us to obtain necessary inputs in empirical applications. In the second part, we estimate a canonical discrete time Gaussian three factor term structure model with the U.S. Treasury bond yields. We decompose bond yields into expectation and risk components without specifying risk adjustment inside the model. The results indicate that power of term spread in predicting economic activity stems from level of expectations component and change in risk premium component. ∗Aydin, [email protected], Istanbul School of Central Banking, The Central Bank of Turkey; Yildirim, [email protected], Zicklin School of Business, Baruch College, CUNY, 137 E 22nd, New York 10010, USA. We thank the seminar participants at Whitman School of Business and Istanbul School of Central Banking for their helpful comments and suggestions.