No-arbitrage Restrictions Research Articles

A Smooth Shadow-Rate Dynamic Nelson-Siegel Model for Yields at the Zero Lower Bound

We propose a smooth shadow-rate version of the dynamic Nelson-Siegel (DNS) model to analyze the term structure of interest rates during a zero lower bound (ZLB) period. By relaxing the no-arbitrage restriction, our shadow-rate model becomes highly tractable with a closed-form yield curve expression. This permits the implementation of readily available DNS extensions such as allowing for time-varying parameters and the integration of macroeconomic variables. Using U.S. Treasury data, we provide clear evidence of a smooth transition of the yields entering and leaving the ZLB state. Moreover, we show that the smooth shadow-rate DNS model dominates the baseline DNS model and (shadow-rate) affine term structure models in terms of fitting and forecasting the yield curve, while it also produces plausible policy insights at the ZLB.

A Large Vector Autoregression of the Yield Curve and Macroeconomic Variables with No-Arbitrage Restriction

A Large Vector Autoregression of the Yield Curve and Macroeconomic Variables with No-Arbitrage Restriction

A penalized two-pass regression to predict stock returns with time-varying risk premia

We develop a penalized two-pass regression with time-varying factor loadings. The penalization in the first pass enforces sparsity for the time-variation drivers while also maintaining compatibility with the no-arbitrage restrictions by regularizing appropriate groups of coefficients. The second pass delivers risk premia estimates to predict equity excess returns. Our Monte Carlo results and our empirical results on a large cross-sectional data set of US individual stocks show that penalization without grouping can yield to nearly all estimated time-varying models violating the no-arbitrage restrictions. Moreover, our results demonstrate that the proposed method reduces the prediction errors compared to a penalized approach without appropriate grouping or a time-invariant factor model.

Bond risk premia in emerging markets: evidence from Brazil, China, Mexico, and Russia

ABSTRACT We employ an affine term structure model with no-arbitrage restrictions and unspanned risk factors to analyse the global and domestic determinants of bond risk premia in four major emerging markets (Brazil, China, Mexico, and Russia). Among the risk factors, we select national inflation and economic growth, and the country-specific nominal exchange rate against the US dollar as the variables related to the domestic economy. We include a measure of worldwide economic activity, the Market Volatility Index (VIX), and an aggregate price index of commodities in the group of global factors. Our model captures (long-term) movements of realized risk premia and indicates that global economic and financial factors play a relevant role in explaining country-specific bond risk premia dynamics. In contrast, domestic variables carry little explanatory power to rationalize risk premia developments in these four economies. We also provide evidence of heterogeneous responses of country-specific risk premia to global and domestic shocks.

The interest rate determination when economic variables are partially observable

While recent studies based on factor models with no-arbitrage restrictions provide evidence of a positive correlation between the nominal interest rates and real activity, there are few dynamic general equilibrium models which can successfully explain this positive relationship. This paper provides a dynamic general equilibrium model that naturally generates a positive correlation between the nominal interest rates and excess consumption. To this end, we focus on the partial observability of economic variables in a pure exchange economy and derive a closed form solution for two-factor affine term structure model. Our empirical analysis based on the results indeed indicates the positive correlation between the nominal interest rates and excess consumption. Moreover, the time series of the model-implied nominal yield captures many of the short- and long-run fluctuations in the actual data.

Interest Rate Volatility and No-Arbitrage Affine Term Structure Models

Within the affine framework, many have observed a tension between matching conditional first and second moments in dynamic term structure models (DTSMs). Although the existence of this tension is generally accepted, less understood is the mechanism that underlies it. We show that no arbitrage along with the rich information in the cross section of yields has strong implications for both the dynamics of volatility and the forecasts of yields. We show that this link implied by the absence of arbitrage—and not the factor structure per se—underlies the tension between first and second moments found in the literature. Adding to recent research that has suggested that no-arbitrage restrictions are nearly irrelevant in Gaussian DTSMs, our results show that no-arbitrage restrictions are potentially relevant when there is stochastic volatility. This paper was accepted by Gustavo Manso, finance.

Exploring Risk Premia, Pricing Kernels, and No-Arbitrage Restrictions in Option Pricing Models

Exploring Risk Premia, Pricing Kernels, and No-Arbitrage Restrictions in Option Pricing Models

The Law of One Price in Equity Volatility Markets

This paper documents law of one price violations in equity volatility markets. While tightly linked by no-arbitrage restrictions, the prices of VIX futures exhibit significant deviations relative to their option-implied upper bounds. Static arbitrage opportunities occur when the prices of VIX futures violate their bounds. The deviations widen during periods of market stress and predict the returns of VIX futures. A relative value trading strategy based on the deviation measure earns a large Sharpe ratio and economically significant alpha-to-margin. There is evidence that systematic risk and demand pressure contribute to the variation in the no-arbitrage deviations over time.

Universal Arbitrage-Free Estimation of State Price Density

Given the valuable information content of Arrow-Debreu prices, the recovery of a well-behaved state price density is of considerable importance. However, this is a nontrivial task because of data limitation and the complex arbitrage-free constraints. In this article, we develop a more effective linear programming support vector machine estimator for state price density, which incorporates no-arbitrage restrictions and bid-ask spread. This method does not depend on a particular approximation function and framework and is, therefore, universally applicable. In a parallel empirical study, we apply the method to options on the S&P 500, showing it to be accurate and smooth. TOPICS:Derivatives, options Key Findings ▪ Recovery of a well-behaved state price density is an important but nontrivial because of data limitation and the complex arbitrage-free constraints. ▪ We develop a universally applicable linear programming support vector machine estimator for state price density that incorporates no-arbitrage restrictions and bid-ask spread. ▪ We apply the method empirically to options on the S&P 500, showing it to be accurate and smooth.

Forecasting the Term Structure of Interest Rates with Dynamic Constrained Smoothing B-Splines

The Nelson–Siegel framework published by Diebold and Li created an important benchmark and originated several works in the literature of forecasting the term structure of interest rates. However, these frameworks were built on the top of a parametric curve model that may lead to poor fitting for sensible term structure shapes affecting forecast results. We propose DCOBS with no-arbitrage restrictions, a dynamic constrained smoothing B-splines yield curve model. Even though DCOBS may provide more volatile forward curves than parametric models, they are still more accurate than those from Nelson–Siegel frameworks. DCOBS has been evaluated for ten years of US Daily Treasury Yield Curve Rates, and it is consistent with stylized facts of yield curves. DCOBS has great predictability power, especially in short and middle-term forecast, and has shown greater stability and lower root mean square errors than an Arbitrage-Free Nelson–Siegel model.

Bond Risk Premia in Emerging Markets: Evidence from Brazil and Uruguay

We employ an affine term structure model with no-arbitrage restrictions to analyze the global and domestic determinants of bond risk premia in major emerging markets. Our model captures (long-term) movements of realized risk premia and indicates that global economic and financial factors play a relevant role in explaining country-specific bond risk premia. We also provide evidence of heterogeneous responses of country-specific risk premia to global shocks.

The effects of conventional and unconventional monetary policy on forecasting the yield curve

We investigate how conventional and unconventional monetary policies affect the dynamics of the yield curve by assessing the performance of individual yield curve models and their mixtures. Out-of-sample forecasts for U.S. bond yields show that the arbitrage-free Nelson–Siegel model and its mixtures with other models perform well in the period of conventional monetary policy, whereas the random walk model outperforms all the other models in the period of unconventional monetary policy. The diminished role of the no-arbitrage restriction in forecasting the yield curve since 2009 can be attributed to unconventional monetary policy, which resulted in low correlations between short- and long-term bond yields and little variation in the short-term rates. During the period of the maturity extension program in 2011–2012, the superiority of the random walk forecasts is more pronounced, reinforcing our finding that the monetary policy framework affects yield curve forecast accuracy.

Estimation of Peru’s sovereign yield curve: the role of macroeconomic and latent factors

PurposeFollowing Ang and Piazzesi’s (2003) study, the authors use an affine term structure model to study the relevance of macroeconomic (domestic and foreign) factors for Peru’s sovereign yield curve in the period from November 2005 to December 2015. The paper aims to discuss this issue.Design/methodology/approachRisk premia are modeled as time-varying and depend on both observable and unobservable factors; and the authors estimate a vector autoregressive model considering no-arbitrage assumptions.FindingsThe authors find evidence that macro factors help to improve the fit of the model and explain a substantial amount of variation in bond yields. However, their influence is very sensitive to the specification model. Variance decompositions show that macro factors explain a significant share of the movements at the short and middle segments of the yield curve (up to 50 percent), while unobservable factors are the main drivers for most of the movements at the long end of the yield curve (up to 80 percent). Furthermore, the authors find that international markets are relevant for the determination of the risk premium in the short term. Higher uncertainty in international markets increases bond yields, although this effect vanishes quickly. Finally, the authors find that no-arbitrage restrictions with the incorporation of macro factors improve forecasts.Originality/valueTo the authors’ knowledge this is the first application of this type of models using data from an emerging country such as Peru.

The arbitrage-free generalized Nelson–Siegel term structure model: Does a good in-sample fit imply better out-of-sample forecasts?

At the zero lower bound, the dynamic Nelson–Siegel (DNS) model and even the Svensson generalization of the model have trouble in fitting the short maturity yields and fail to grasp the characteristics of the Japanese government bonds (JGBs) yield curve. During the zero interest rate policy regime, the short end of the yield curve is flat and yields corresponding to various maturities have asymmetric movements. Therefore, closely related generalized versions of Nelson–Siegel model—with and without no-arbitrage restriction (GAFNS and GDNS)—that have two slopes and curvatures factors are considered and compared empirically in terms of in-sample fit as well as out-of-sample forecasts with the standard Nelson–Siegel model—with and without no-arbitrage restriction (AFNS and DNS). The affine-based models provide a more attractive fit of the yield curve than their counterpart DNS-based models. Both extended models are capable to restrict the estimated rates from becoming negative at the short end of the curve and distill the JGBs term structure of interest rate quite well. The affine-based extended model leads to a better in-sample fit than the simple GDNS model. In terms of out-of-sample accuracy, both non-affine models outperform the affine models at least for 1- and 6-month horizons. The out-of-sample predictability of the GDNS for the 1- and 6-month-ahead forecasts is superior to the GAFNS for all maturities, and for longer horizons, i.e., 12-month-ahead, the former is still compatible to the latter, particularly for short- and medium-term maturities.

Comparing Asset Pricing Models by the Conditional Hansen-Jagannathan Distance*

AbstractWe compare nonnested parametric specifications of the stochastic discount factor (SDF) using the conditional Hansen–Jagannathan (HJ-) distance. This distance measures the discrepancy between a parametric model-implied SDF and the admissible SDF’s satisfying all the conditional (dynamic) no-arbitrage restrictions, instead of just few unconditional no-arbitrage restrictions for managed portfolios chosen through the instrument selection. We estimate the conditional HJ-distance by a generalized method of moments estimator and establish its large sample properties for model selection purposes. We compare empirically several SDF models including multifactor beta pricing specifications and some recently proposed SDF models that are conditionally linear in consumption growth.

The Effects of Conventional and Unconventional Monetary Policy on Forecasting the Yield Curve

We investigate how conventional and unconventional monetary policies affect the dynamics of the yield curve by assessing the performance of individual yield curve models and their mixtures. Out-of-sample forecasts for U.S. bond yields show that the arbitrage-free Nelson-Siegel model and its mixtures with other models perform well in the period of conventional monetary policy, whereas the random walk model outperforms all the other models in the period of unconventional monetary policy. The diminished role of the no-arbitrage restriction in forecasting the yield curve since 2009 can be attributed to unconventional monetary policy, which resulted in low correlations between short- and long-term bond yields and little variation in the short-term rates. During the period of the maturity extension program in 2011--2012, the superiority of the random walk forecasts is more pronounced, reinforcing our finding that the monetary policy framework affects yield curve forecast accuracy.

INFERENCE FOR OPTION PANELS IN PURE-JUMP SETTINGS

We develop parametric inference procedures for large panels of noisy option data in a setting, where the underlying process is of pure-jump type, i.e., evolves only through a sequence of jumps. The panel consists of options written on the underlying asset with a (different) set of strikes and maturities available across the observation times. We consider an asymptotic setting in which the cross-sectional dimension of the panel increases to infinity, while the time span remains fixed. The information set is augmented with high-frequency data on the underlying asset. Given a parametric specification for the risk-neutral asset return dynamics, the option prices are nonlinear functions of a time-invariant parameter vector and a time-varying latent state vector (or factors). Furthermore, no-arbitrage restrictions impose a direct link between some of the quantities that may be identified from the return and option data. These include the so-called jump activity index as well as the time-varying jump intensity. We propose penalized least squares estimation in which we minimize the L2 distance between observed and model-implied options. In addition, we penalize for the deviation of the model-implied quantities from their model-free counterparts, obtained from the high-frequency returns. We derive the joint asymptotic distribution of the parameters, factor realizations and high-frequency measures, which is mixed Gaussian. The different components of the parameter and state vector exhibit different rates of convergence, depending on the relative (asymptotic) informativeness of the high-frequency return data and the option panel.

Bond Portfolio Optimization in the Presence of Duration Constraints

Although there exists an abundant literature on the benefits and limits of scientific diversification in the equity universe, little is known about the out-of-sample performance of portfolio optimization models in the fixed-income universe. In this article, the authors address two key challenges that are specific to bond portfolio optimization, namely, the presence of duration constraints and the presence of no-arbitrage restrictions on risk parameter estimates, for which no equivalent exists in the equity universe. In an application to sovereign bonds in the eurozone, they find that the use of portfolio optimization techniques based on robust estimators for risk parameters generates an improvement in investor welfare compared with the use of ad hoc bond benchmarks such as equally weighted or cap-weighted portfolios. These results are robust with respect to changes in the number of constituents in the portfolio and the rebalancing period, and in the presence of duration or weight constraints. <b>TOPICS:</b>Fixed income and structured finance, fixed-income portfolio management, statistical methods

PutWrite versus BuyWrite: Yes, Put-Call Parity Holds Here Too

The CBOE PutWrite Index has outperformed the BuyWrite Index by approximately 1.1 percent per year between 1986 and 2015. That is pretty impressive. But troubling. Yes – troubling – because the theory of put-call parity tells us that such outperformance should be almost impossible via a compelling no-arbitrage restriction. This paper explains the mystery of this outperformance, which has implications for portfolio construction.

A Gaussian Affine Term Structure Model of Interest Rates and Credit Spreads

We estimate a no-arbitrage term structure model of U.S. Treasury yields and corporate bond spreads with both economic factors and latent factors as drivers of term structure dynamics. We consider two sets of economic factors: macro factors consisting of inflation and real activity, and financial market factors consisting of funding liquidity and market volatility. We show that financial market factors have limited effects on the Treasury yield curve but substantial impacts on the credit spread term structure. In particular, negative liquidity shocks widen credit spreads, and this effect is more pronounced for short-term corporate bonds. We also find that out-of-sample forecasts for credit spreads improve when financial market factors are incorporated and when no-arbitrage restrictions are imposed. We also propose a minimum-chi-square method for estimating the term structure models of interest rate and credit spreads, which is more efficient and accurate than the widespread maximum-likelihood estimation.