The Role of Jumps and Options in the Risk Premia of Interest Rates

There is evidence that jumps double the explanatory power of Campbell and Shiller (1991) excess bond returns’ regressions (Wright and Zhou, 2009), and options bring information about bond risk premia beyond that spanned by the yield curve (Joslin, 2007). In this paper I incorporate these features in a Gaussian Affine Term Structure Model (ATSM) in order to assess two questions: (1) what are the implications of incorporating jumps in an ATSM for option pricing, and (2) how jumps and options affect the bond risk-premia dynamics.The main findings are: (1) jump risk-premia is negative in a scenario of decreasing interest rates, and has a significant average magnitude of 1% to 2%, which means that, it explains 10% to 20% of the level of the yields; (2) the Gaussian model (A30) and the Gaussian model with constant intensity jumps (A30J) are the ones that best fit the option prices; and (3) the Gaussian model with constant intensity jumps estimated jointly with options (A30oJ) is the one that best identifies the risk premium.