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Nonparametric Interest Rate Cap Pricing: Implications for the ‘‘Unspanned Stochastic Volatility“ Puzzle


  • Acknowledgments: I gratefully acknowledge many helpful discussions with Michael Brandt and Amir Yaron. I also thank participants at the 16th Derivatives Securities and Risk Management Conference at the Federal Deposit Insurance Corporation and SoFiE Third Annual Meeting. All remaining weaknesses are of course my own.

Corresponding author: Tao L. Wu, Stuart School of Business, Illinois Institute of Technology, 565 W. Adams Street, Chicago, IL 60661, USA. Tel: +312-9066553, Fax: +312-9066549, email:


Asset prices depend on two elements: the dynamics of the state variables and the pricing kernel. Traditional term structure models differ in 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 interest rate cap prices are very sensitive to the specification of factor dynamics, especially when they are close to expiration. In addition, nonlinear log-pricing kernels improve the pricing of long-maturity caps, although significant pricing errors remain. Recent published studies document models that fit the London Inter-Bank offer Rate (LIBOR) and swap rates but do not price derivatives well, leading to the so-called ‘‘unspanned stochastic volatility puzzle.” Additional volatility 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-specifications of the parametric models used. Our paper provides evidence for unspanned stochastic volatility from a nonparametric perspective.