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

Author

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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.

Suggested Citation

  • Haitao Li & Feng Zhao, 2009. "Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4335-4376, November.
    • Handle: RePEc:oup:rfinst:v:22:y:2009:i:11:p:4335-4376
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    References listed on IDEAS

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