Implied volatility term structure and exchange rate predictability

This paper provides empirical evidence of the predictive power of the currency implied volatility term structure (IVTS) for the behavior of the exchange rate from both cross-sectional and time series perspectives. Intriguingly, the direction of the prediction is not the same for developed and emerging markets. For developed markets, a high slope means low future returns, while for emerging markets it means high future returns. We analyze predictability from a cross-sectional perspective by building portfolios based on the slope of the term structure, and thus present a new currency trading strategy. For developed (emerging) currencies, we buy (sell) the two currencies with the lowest slopes and sell (buy) the two with the highest slopes. The proposed strategy performs better than common currency strategies – carry trade, risk reversal, and volatility risk premium (VRP) – based on the Sharpe ratio, considering only currency returns, which supports the exchange rate predictability of the IVTS from a cross-sectional perspective.     

A note on direct term structure estimation using monotonic splines

A monotonic spline parametrization is proposed as a reliable alternative to the traditional Bernstein-based approach for Direct Term Structure Estimation. Numerical experiments with Italian bond data demonstrate the effectiveness of the proposed method.     

Evolving macroeconomic perceptions and the term structure of interest rates

We explore the role of evolving beliefs regarding the structure of the macroeconomy in improving our understanding of the term structure of interest rates within the context of a simple macro-finance model. Using quarterly vintages of real-time data and survey forecasts for the United States over the past 40 years, we show that a recursively estimated VAR on real GDP growth, inflation and the nominal short-term interest rate generates predictions that are more consistent with survey forecasts than a benchmark fixed-coefficient counterpart. We then estimate a simple term structure model under the assumption that investor risk attitude is driven by near-term expectations of the three state variables. When we allow for evolving beliefs about the macroeconomy, the resulting term structure model provides a better fit to the cross section of yields than the benchmark model, especially at longer maturities, and exhibits better performance in out-of-sample predictions of future yield movements.     

Discrete time Wishart term structure models

This paper reveals that the class of Affine Term Structure Models (ATSMs) introduced by Duffie and Kan (1996) is larger than previously considered in the literature. In the framework of risk factors following a Wishart autoregressive process, we define the Wishart Term Structure Model (WTSM) as an extension of a subclass of Quadratic Term Structure Models (QTSMs), derive simple parameter restrictions that ensure positive bond yields at all maturities, and observe that the usual constraint on affine processes requiring that the volatility matrix be diagonal up to a path independent linear invertible transformation can be considerably relaxed.     

Term structure estimation in the presence of autocorrelation

This paper assesses the effects of autocorrelation on parameter estimates of affine term structure models (ATSM) when principal components analysis is used to extract factors. In contrast to recent studies, we design and run a Monte Carlo experiment that relies on the construction of a simulation design that is consistent with the data, rather than theory or observation, and find that parameter estimation from ATSM is precise in the presence of serial correlation in the measurement error term. Our findings show that parameter estimation of ATSM with principal component based factors is robust to autocorrelation misspecification.     

Measuring the natural rate of interest: A note on transitory shocks

We present evidence that the natural rate of interest is buffeted by both permanent and transitory shocks. We establish this result by estimating a benchmark model with Bayesian methods and loose priors on the unobserved drivers of the natural rate. When subject to transitory shocks, the median estimate for the US economy is more procyclical, displays a less marked secular decline, and is therefore higher following the Great Recession than most estimates in the literature.     

Gradient-based smoothing parameter selection for nonparametric regression estimation

Estimating gradients is of crucial importance across a broad range of applied economic domains. Here we consider data-driven bandwidth selection based on the gradient of an unknown regression function. This is a difficult problem given that direct observation of the value of the gradient is typically not observed. The procedure developed here delivers bandwidths which behave asymptotically as though they were selected knowing the true gradient. Simulated examples showcase the finite sample attraction of this new mechanism and confirm the theoretical predictions.     

Estimation of affine term structure models with spanned or unspanned stochastic volatility

We develop new procedures for maximum likelihood estimation of affine term structure models with spanned or unspanned stochastic volatility. Our approach uses linear regression to reduce the dimension of the numerical optimization problem yet it produces the same estimator as maximizing the likelihood. It improves the numerical behavior of estimation by eliminating parameters from the objective function that cause problems for conventional methods. We find that spanned models capture the cross-section of yields well but not volatility while unspanned models fit volatility at the expense of fitting the cross-section.     

A note on estimation based on record data

In data-processing standpoint, an efficient algorithm for identifying the minimum value among a set of measurements are record statistics. From a sequence of n independent identically distributed continuous random variables only about log(n) records are expected, so we expect to have little data, hence any prior information is welcome (Houchens, Record value theory and inference, Ph.D. thesis, University of California, Riverside, 1984). In this paper, non-Bayesian and Bayesian estimates are derived for the two parameters of the Exponential distribution based on record statistics with respect to the squared error and Linear-Exponential loss functions and then compared with together. The admissibility of some estimators is discussed.     

A note on consistency and unbiasedness of point estimation with fuzzy data

Based on the SLLN for fuzzy random variables in uniform metric d, some asymptotical properties of point estimation with fuzzy random samples are investigated. The results of this paper establish a corresponding version on the consistency and unbiasedness of point estimation with n-dimensional fuzzy samples under considering a kind of fuzzy statistic.     

Bond risk, bond return volatility, and the term structure of interest rates

This paper explores the time variation in the bond risk, as measured by the covariation of bond returns with stock returns and consumption growth, and in the volatility of bond returns. A robust stylized fact in empirical finance is that the spread between the yields on long- and short-term bonds forecasts future excess returns on bonds at varying horizons positively; in addition, the short-term nominal interest rate forecasts both the stock return volatility and the exchange rate volatility positively. This paper presents evidence that movements in both the short-term nominal interest rate and the yield spread are positively related to changes in the subsequent realized bond risk and bond return volatility. The yield spread appears to proxy for business conditions, while the short rate appears to proxy for inflation and economic uncertainty. A decomposition of bond betas into a real cash flow risk component and a discount rate risk component shows that yield spreads have offsetting effects in each component. A widening yield spread is correlated with a reduced cash-flow (or inflationary) risk for bonds, but it is also correlated with a larger discount rate risk for bonds. The short rate only forecasts the discount rate component of the bond beta.     

Physics-informed Gaussian process regression for states estimation and forecasting in power grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method.We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power.For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.     

A note on multinomial maximum likelihood estimation under ordered restrictions and the EM algorithm

A frequently occurring problem is to find the maximum likelihood estimation (MLE) of p subject to p∈C (C⊂ P the probability vectors in R ^k ). The problem has been discussed by many authors and they mainly focused when p is restricted by linear constraints or log-linear constraints. In this paper, we construct the relationship between the the maximum likelihood estimation of p restricted by p∈C and EM algorithm and demonstrate that the maximum likelihood estimator can be computed through the EM algorithm (Dempster et al. in J R Stat Soc Ser B 39:1–38, 1997). Several examples are analyzed by the proposed method.     

Processes with volatility-induced stationarity: an application for interest rates

In this paper we propose a refinement of the existing definition of volatility-induced stationarity that allows us to distinguish between processes with drift and diffusion induced stationarity and processes with pure volatility-induced stationarity. We also propose a classification of stationary processes with volatility-induced stationarity according to the volatility that is needed to inject stationarity. Processes with volatility-induced stationarity are potentially applicable to interest rate time-series since, as has been acknowledged, mean-reversion effects occur mainly in periods of high volatility. As such, we provide evidence that the logarithm of the Fed funds rate can be modelled as a local martingale with volatility-induced stationarity.     

A tale of two yield curves: Modeling the joint term structure of dollar and euro interest rates

Modeling the joint term structure of interest rates in the United States and the European Union, the two largest economies in the world, is extremely important in international finance. In this article, we provide both theoretical and empirical analysis of multi-factor joint affine term structure models (ATSM) for dollar and euro interest rates. In particular, we provide a systematic classification of multi-factor joint ATSM similar to that of Dai and Singleton (2000). A principal component analysis of daily dollar and euro interest rates reveals four factors in the data. We estimate four-factor joint ATSM using the approximate maximum likelihood method of [A?t-Sahalia, 2002] and [A?t-Sahalia, forthcoming] and compare the in-sample and out-of-sample performances of these models using some of the latest nonparametric methods. We find that a new four-factor model with two common and two local factors captures the joint term structure dynamics in the US and the EU reasonably well.     

Spline regression for hazard rate estimation when data are censored and measured with error

In this paper, we study an estimation problem where the variables of interest are subject to both right censoring and measurement error. In this context, we propose a nonparametric estimation strategy of the hazard rate, based on a regression contrast minimized in a finite‐dimensional functional space generated by splines bases. We prove a risk bound of the estimator in terms of integrated mean square error and discuss the rate of convergence when the dimension of the projection space is adequately chosen. Then we define a data‐driven criterion of model selection and prove that the resulting estimator performs an adequate compromise. The method is illustrated via simulation experiments that show that the strategy is successful.     

Forecasts of US short-term interest rates: A flexible forecast combination approach

This paper develops a flexible approach to combine forecasts of future spot rates with forecasts from time-series models or macroeconomic variables. We find empirical evidence that, accounting for both regimes in interest rate dynamics, and combining forecasts from different models, helps improve the out-of-sample forecasting performance for US short-term rates. Imposing restrictions from the expectations hypothesis on the forecasting model are found to help at long forecasting horizons.     

A general framework for frontier estimation with panel data

The main objective of the paper is to present a general framework for estimating production frontier models with panel data. A sample of firms i = 1, ..., N is observed on several time periods t = 1, ... T. In this framework, nonparametric stochastic models for the frontier will be analyzed. The usual parametric formulations of the literature are viewed as particular cases and the convergence of the obtained estimators in this general framework are investigated. Special attention is devoted to the role of N and of T on the speeds of convergence of the obtained estimators. First, a very general model is investigated. In this model almost no restriction is imposed on the structure of the model or of the inefficiencies. This model is estimable from a nonparametric point of view but needs large values of T and of N to obtain reliable estimates of the individual production functions and estimates of the frontier function. Then more specific nonparametric firm effect models are presented. In these cases, only NT must be large to estimate the common production function; but again both large N and T are needed for estimating individual efficiencies and for estimating the frontier. The methods are illustrated through a numerical example with real data.