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

Posted: 8 Dec 2009

See all articles by Haitao Li

Haitao Li

University of Michigan - Stephen M. Ross School of Business; Cheung Kong Graduate School of Business; Cheung Kong Graduate School of Business

Feng Zhao

University of Texas at Dallas - Jindal School of Management

Date Written: November 2009

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.

JEL Classification: G12, G13

Suggested Citation

Li, Haitao and Zhao, Feng, Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices (November 2009). The Review of Financial Studies, Vol. 22, Issue 11, pp. 4335-4376, 2009, Available at SSRN: https://ssrn.com/abstract=1519273 or http://dx.doi.org/hhp025

Haitao Li (Contact Author)

University of Michigan - Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States
734-615-5475 (Phone)

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Feng Zhao

University of Texas at Dallas - Jindal School of Management ( email )

800 W. Campbell Rd. SM 31
Richardson, TX 75080
United States
972-883-5815 (Phone)

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