Negative real interest rates
针对标准模型无法处理负实际利率的问题，用皮尔逊IV型概率密度重新表述技术不确定性变量，推导出瞬时实际利率的条件矩和纯贴现债券定价公式，实证表明英美短期国债实际利率与该模型高度吻合。
Standard textbook general equilibrium term structure models such as that developed by Cox, Ingersoll, and Ross [1985b. “A Theory of the Term Structure of Interest Rates.” Econometrica 53 (2): 385–407], do not accommodate negative real interest rates. Given this, the Cox, Ingersoll, and Ross [1985b. “A Theory of the Term Structure of Interest Rates.” Econometrica 53 (2): 385–407] ‘technological uncertainty variable’ is formulated in terms of the Pearson Type IV probability density. The Pearson Type IV encompasses mean-reverting sample paths, time-varying volatility and also allows for negative real interest rates. The Fokker–Planck (i.e. the Chapman–Kolmogorov) equation is then used to determine the conditional moments of the instantaneous real rate of interest. These enable one to determine the mean and variance of the accumulated (i.e. integrated) real rate of interest on a bank (or loan) account when interest accumulates at the instantaneous real rate of interest defined by the Pearson Type IV probability density. A pricing formula for pure discount bonds is also developed. Our empirical analysis of short-dated Treasury bills shows that real interest rates in the UK and the USA are strongly compatible with a general equilibrium term structure model based on the Pearson Type IV probability density.