RFS Advance Access originally published online on April 10, 2009
Review of Financial Studies 2009 22(11):4335-4376; doi:10.1093/rfs/hhp025
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Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices
Stephen M. Ross School of Business, University of Michigan
University of Texas at Dallas
Send correspondence to either Haitao Li, Stephen M. Ross School of Business, University of Michigan, Ann Arbor, MI 48109; telephone: 734-615-5475; fax: 734-936-8716. E-mail: htli{at}umich.edu, or Feng Zhao, School of Management, University of Texas at Dallas, Richardson, TX 75080; telephone: 972-883-5815, fax: 972-883-2799. E-mail: feng.zhao{at}utdallas.edu.
JEL Classification: G12, G13
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Abstract |
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Based on a multivariate extension of the constrained locally polynomial estimator of Aït-Sahalia and Duarte (2003), we provide one of the first nonparametric estimates of probability densities of LIBOR rates under forward martingale measures and state-price densities (SPDs) implicit in interest rate cap prices. The forward densities and SPDs depend significantly on the slope and volatility of LIBOR rates, and mortgage markets activities have strong impacts on the shape of the forward densities. The SPDs exhibit a pronounced U-shape as a function of future LIBOR rates, suggesting that the state prices are high at both extremely low and high interest rates, which tend to be associated with recessions and periods of high inflation, respectively. Our results provide nonparametric evidence of unspanned stochastic volatility and suggest that the unspanned factors could be partly driven by activities in the mortgage markets.
We thank Yacine Aït-Sahalia (the editor), David Bates, Ivan Brick, Dennis Capozza, Ren-Raw Chen, Ted Day, Jefferson Duarte, Tom George, Yongmiao Hong, Robert Jarrow, Robert Kieschnick, Frank Nothaft, Stuart Turnbull, Bob Van Order, Yexiao Xu, Yuewu Xu, An Yan, Harold Zhang, Jin Zhang, an anonymous referee, and seminar participants at Rutgers University, the University of Houston, the University of Iowa, the University of Texas at Dallas, the 17th Derivatives Conference at FDIC, the 2007 China International Conference in Finance, the 2008 Econometric Society North American Meeting, and the first Triple Crown Conference in Finance for helpful discussions. We are responsible for any remaining errors.