Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices
扩展了Aït-Sahalia和Duarte的约束局部多项式估计方法，首次非参数估计了LIBOR利率在远期鞅测度下的概率密度和隐含在利率上限期权中的状态价格密度，发现其形状受利率斜率、波动率和抵押贷款市场活动显著影响。
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.