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This paper employs an approximation that makes a nonlinear term structure model extremely tractable for analysis of an economy operating near the zero lower bound for interest rates. We show that such a model offers an excellent description of the data compared to the benchmark model and can be used to summarize the macroeconomic effects of unconventional monetary policy. Our estimates imply that the efforts by the Federal Reserve to stimulate the economy since July 2009 succeeded in making the unemployment rate in December 2013 1% lower, which is 0.13% more compared to the historical behavior of the Fed.

We show that conventional dynamic term structure models (DTSMs) estimated on recent U.S. data severely violate the zero lower bound (ZLB) on nominal interest rates and deliver poor forecasts of future short rates. In contrast, shadow-rate DTSMs account for the ZLB by construction, capture the resulting distributional asymmetry of future short rates, and achieve good forecast performance. These models provide more accurate estimates of the most likely path for future monetary policy—including the timing of policy liftoff from the ZLB and the pace of subsequent policy tightening. We also demonstrate the benefits of including macroeconomic factors in a shadow-rate DTSM when yields are constrained near the ZLB.

Shadow short rate (SSR) estimates are generated regressors proposed as a proxy for policy interest rates during unconventional monetary policy (UMP) periods. However, using the Wu and Xia (2016) shadow/lower-bound model, I show that SSR estimates can be sensitive to minor choices in their estimation. Used subsequently in a small macroeconomic model, those sensitivities lead to wide variations in the inferred effects of UMP on inflation and unemployment outcomes. Therefore, it should not be presumed that any SSR series will necessarily be quantitatively useful. Vetting SSR series allows appropriate SSR series to be retained within the suite of UMP indicators.

The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed-income applications. We investigate whether the unscented Kalman filter should be used to capture nonlinearities and compare the performance of the Kalman filter with that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also performs well when compared with the much more computationally intensive particle filter. These findings suggest that the unscented Kalman filter may be a good approach for a variety of problems in fixed-income pricing. This paper was accepted by Wei Xiong, finance .

We present a new term-structure model for commodity futures prices based on Trolle and Schwartz (2009), which we extend by incorporating seasonal stochastic volatility represented with two different sinusoidal expressions. We obtain a quasi-analytical representation of the characteristic function of the futures log-prices and closed-form expressions for standard European options’ prices using the fast Fourier transform algorithm. We price plain vanilla options on the Henry Hub natural gas futures contracts, using our model and extant models. We obtain higher accuracy levels with our model than with the extant models.

Existing results show that (i) lagged forward rates help predict bond returns and (ii) modern Markovian dynamic term structure models (DTSMs) cannot match the evidence [Cochrane JH, Piazzesi M (2005) Bond risk premia. Amer. Econom. Rev. 95(1):138–160]. We develop the family of conditional mean DTSMs where the dynamics depend on current yields and their history through a moving-average component. Our preferred conditional mean model combines one moving average with the usual three Gaussian risk factors, closely matches the bond risk premium measured from predictive regressions, and provides better forecasts of bond returns. Our framework nests Duffee’s models with a small “hidden” factor [Duffee G (2011) Information in (and not in) the term structure. Rev. Financial Stud. 24(9):2895–2934], and our results compare favorably with his five-factor model. Conditional mean models are easier to estimate than state-space term structure models based on Kalman estimates of latent factors. The online appendix is available at https://doi.org/10.1287/mnsc.2016.2602 . This paper was accepted by Lauren Cohen, finance.

This study adopts a three-factor approach to the affine term structure models, aiming to analyse South African (SA) government bond yields across various maturities. The primary objective is to evaluate whether these models offer robust pricing capabilities—being both admissible and flexible—while capturing the conditional correlations and volatilities of yield factors specific to SA bond yields. For a model to be considered admissible, it must also demonstrate economic identification and maximal flexibility. We thus investigate the short-, medium-, and long-term dynamics of bond yields concurrently. Model estimation involves deriving joint conditional densities through the inversion of the Fourier transform applied to the characteristic function of the state variables. This enables the use of maximum likelihood estimation as an efficient method. We assume that the market prices of risk are proportional to the volatilities of the state variables. The analysis reveals negative correlations between factors. Among the models tested, the A1(3) model outperforms the A2(3) model in terms of fit, both in sample and out of sample.

This paper presents weak second and third order schemes for the Cox-Ingersoll-Ross (CIR) process, without any restriction on its parameters. At the same time, it gives a general recursive construction method for getting weak second order schemes that extend the one introduced by Ninomiya and Victoir. Combine both these results, this allows us to propose a second order scheme for more general affine diffusions. Simulation examples are given to illustrate the convergence of these schemes on CIR and Heston models.

We introduce a class of interest rate models, called the α -CIR model, which is a natural extension of the standard CIR model by adding a jump part driven by α -stable Lévy processes with index α ∈ ( 1 , 2 ] . We deduce an explicit expression for the bond price by using the fact that the model belongs to the family of CBI and affine processes, and analyze the bond price and bond yield behaviors. The α -CIR model allows us to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rates together with the presence of large jumps. Finally, we provide a thorough analysis of the jumps, and in particular the large jumps.

In this paper, we present a robust predictive comparison of several continuous-time multi-factor models in the context of interbank rates. Recognizing the specific dynamics of the short-term segment of the yield curve, we examine the U.S. money market by extending two continuous-time frameworks with different factor structures, the Chan-Karolyi-Longstaff-Sanders (CKLS) model and the arbitrage-free dynamic Nelson-Siegel (AFDNS) model. A battery of formal forecasting accuracy tests is employed to select a subset of superior predictive models. Despite a better goodness-of-fit measure, additional factors improve the forecasting performance only for the CKLS family. With implications for monetary policy formulation, we found evidence of two separate maturity segments as the three-factor AFDNS and the five-factor CKLS models outperform parsimonious benchmarks in predicting the interbank rates for very short maturities. Our comparative forecasting results are re-confirmed with stronger out-of-sample performance for the five-factor CKLS model when the post global financial crisis sub-sample is analyzed.