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Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices

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  • Haitao Li
  • Feng Zhao

Abstract

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. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Studies in its journal The Review of Financial Studies.

Volume (Year): 22 (2009)
Issue (Month): 11 (November)
Pages: 4335-4376

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Handle: RePEc:oup:rfinst:v:22:y:2009:i:11:p:4335-4376

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Cited by:
  1. Wolfgang Karl Härdle & Brenda López-Cabrera & Huei-Wen Teng, 2013. "State Price Densities implied from weather derivatives," SFB 649 Discussion Papers SFB649DP2013-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. repec:wyi:wpaper:002044 is not listed on IDEAS
  3. Leippold, Markus & Strømberg, Jacob, 2014. "Time-changed Lévy LIBOR market model: Pricing and joint estimation of the cap surface and swaption cube," Journal of Financial Economics, Elsevier, vol. 111(1), pages 224-250.
  4. Li, Gang & Zhang, Chu, 2013. "Diagnosing affine models of options pricing: Evidence from VIX," Journal of Financial Economics, Elsevier, vol. 107(1), pages 199-219.
  5. Kitsul, Yuriy & Wright, Jonathan H., 2013. "The economics of options-implied inflation probability density functions," Journal of Financial Economics, Elsevier, vol. 110(3), pages 696-711.

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