Nonparametric Interest Rate Cap Pricing and Implications for the “Unspanned Stochastic Volatility ” Puzzle

Asset prices depend on two elements: the dynamics of the state variables and the pricing kernel. Traditional term structure models differ in the factor dynamics. However, most of them imply a log-linear pricing kernel. We investigate empirically the role of factor dynamics and pricing kernel in pricing interest rate derivatives using a nonparametric approach. We find that the prices of interest rate caps are very sensitive to the specification of the factor dynamics, especially when they are close to expiration. In addition, nonlinear log-pricing kernels improve the pricing of long-maturity caps. Recent research document models that fit libor and swap rates but do not price derivatives well, leading to the so called “unspanned stochastic volatility puzzle”. Additional factors seem to be needed to explain cap prices. However, the relative mispricing between interest rate caps and underlying libor and swap rates could also potentially be due to mis-specification of the parametric models used. Our paper provides evidence, from a nonparametric perspective, for the inability of diffusion-only type of models to price interest rate caps. Models with jumps such as that in Jarrow, Li, and Zhao (JF, forthcoming) is needed to explain the prices of libor options