Nonparametric Estimation of State-Price Densities Using Interest Rate Options
We provide one of the first nonparametric estimates of the probability densities of LIBOR rates under forward martingale measures and the state-price densities (SPDs) using interest rate cap prices. We extend the constrained local polynomial approach of Ait-Sahalia and Duarte (2003) to a multivariate setting and estimate the forward densities and the SPDs conditional on the level, slope, and volatility of the LIBOR rates. The multivariate constrained local polynomial approach has excellent finite sample performances and guarantees that the nonparametric estimates satisfy necessary theoretical restrictions. We find that the forward densities deviate significantly from the log-normal distribution and are strongly negatively skewed. The SPDs exhibit a pronounced U-shape as a function of future LIBOR rates. This suggests that the state prices are high at low and high interest rates, which tend to correspond to economic recessions and high inflations, respectively. Both the forward densities and the SPDs depend significantly on the volatility of the LIBOR rates, suggesting that it is important to incorporate unspanned stochastic volatility into equilibrium term structure models.
Haitao Li Feng Zhao
Stephen M.Ross School of Business,University of Michigan
国际会议
成都
英文
2007-07-09（万方平台首次上网日期，不代表论文的发表时间）