Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model

Affine Term Structure Models

“…Cox et al (1985), Gibbons and Ramaswamy (1993), Pearson and Sun (1994), and Heston (1991) assume that m t+τ and 1/p t+τ are independent. This assumption leads to…”

“…In this sense, labels from fundamentals are often empty labels. For example, Pearson and Sun (1994) use the model mentioned by Cox et al (1985) in Section 7 with exogenously specified "expected inflation." Their estimation does not use any data on inflation, however, only data on yields.…”

“…Other applications leave the contaminated yields out and then use them for an out-of-sample check of the model. To be clear, the check is "out-of-sample" only in the cross section,because these are yields not included in the estimation,not in the time-series sense (e.g., Dai and Singleton, 2000;Pearson and Sun, 1994;Piazzesi, 2005).…”

“…The speed of this loop can be increased considerably by supplying the analytical gradient ∂yc (τ) t /∂x t to the gradient-based method that inverts the pricing map. For example, Pearson and Sun (1994) use prices of traded Treasuries in their estimation.…”

A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables

“…Many term structure models have used latent factor models to explain term structure movements, and although there are some interpretations to what these factors mean, the factors are not given direct comparisons with macroeconomic variables. For example, Pearson and Sun (1994)'s factors are labeled "short rate" and "inflation", but their estimation does not use inflation data. The terms "short rate" and "inflation" are just convenient names for the unobserved factors.…”