Fractional Integration and the Dynamics of UK Unemployment*

This article is concerned with estimating the dynamic behaviour of UK unemployment using fractional integration methods. The question it considers is whether an unemployment model using a relatively small set of determinants of unemployment is consistent with the persistence which estimates an integrated model yield, or the much long‐lasting estimates obtained from fractional integration. Our empirical tests favour the latter version. The results show that when accounting for UK unemployment in terms of lagged values of the real oil price and the real interest rate, unemployment appears fractionally integrated. This finding means that although unemployment is mean reverting, once it is shocked it may take a very long time to recover, and our estimates of the response times are considerably in excess of those previously reported in the literature.     

Locally best tests for Gaussian processes

A continuous-time stochastic process occuring in a representation of the likelihood ratio process for Gaussian processes with common covariance kernel is shown to be a Wiener process with respect to a certain family of -algebras. This is applied to the problem of sequentially testing one-sided hypotheses for Gaussian processes, and it is proved that certain continuous-time SPRT's are locally best sequential tests under some restrictions.     

Asset pricing with loss aversion

The use of standard preferences for asset pricing has not been very successful in matching asset price characteristics, such as the risk-free interest rate, equity premium and the Sharpe ratio, to time series data. Behavioral finance has recently proposed more realistic preferences such as those with loss aversion. Research is starting to explore the implications of behaviorally founded preferences for asset price characteristics. Encouraged by some studies of Benartzi and Thaler [1995. Myopic loss aversion and the equity premium puzzle. The Quarterly Journal of Economics 110 (1), 73–92] and Barberis et al. [2001. Prospect theory and asset prices. Quarterly Journal of Economics CXVI (1), 1–53] we study asset pricing with loss aversion in a production economy. Here, we employ a stochastic growth model and use a stochastic version of a dynamic programming method with an adaptive grid scheme to compute the above mentioned asset price characteristics of a model with loss aversion in preferences. As our results show using loss aversion we get considerably better results than one usually obtains from pure consumption-based asset pricing models including the habit formation variant.     

What determines the long-term correlation between oil prices and exchange rates?

In this study, we obtain the long-term correlation between oil prices and exchange rates by employing the dynamic conditional correlation-mixed data sampling (DCC-MIDAS) model. We then identify the factors that influence the long-term correlation using panel data analysis. We find that the long-run correlations between oil prices and exchange rates are negative for all oil-exchange rate markets except Japan. We also find that both inflation and term spread have negative effects, while the risk-free interest rate has a positive effect on the long-term correlation between oil prices and exchange rates. Importantly, the empirical results show that an increase in inflation will significantly damage the real value of the currency itself.     

Implied volatility and the risk-free rate of return in options markets

We numerically solve systems of Black–Scholes formulas for implied volatility and implied risk-free rate of return. After using a seemingly unrelated regressions (SUR) model to obtain point estimates for implied volatility and implied risk-free rate, the options are re-priced using these parameters. After repricing, the difference between the market price and model price is increasing in time to expiration, while the effect of moneyness and the bid-ask spread are ambiguous. Our varying risk-free rate model yields Black–Scholes prices closer to market prices than the fixed risk-free rate model. In addition, our model is better for predicting future evolutions in model-free implied volatility as measured by the VIX.     

Parameter estimation and bias correction for diffusion processes

This paper considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter, as observed in previous studies, we first develop expansions for the bias and variance of parameter estimators for two of the most employed interest rate processes, Vasicek and CIR processes. Then, we study the first order approximate maximum likelihood estimator for linear drift processes. A parametric bootstrap procedure is proposed to correct bias for general diffusion processes with a theoretical justification. Simulation studies confirm the theoretical findings and show that the bootstrap proposal can effectively reduce both the bias and the mean square error of parameter estimates, for both univariate and multivariate processes. The advantages of using more accurate parameter estimators when calculating various option prices in finance are demonstrated by an empirical study.     

Dupire’s formulas in the Piterbarg option pricing model

In this paper we derive an expression for the local volatility of an underlying asset, given the prices of liquid European call options under the Piterbarg framework. The Piterbarg framework is a multi-curve derivative pricing model which extends the well known Black–Scholes–Merton model by relaxing the assumption of a risk-free interest rate, and includes collateral payments. The expressions for the local volatility is a function of the option price surface, and is then transformed to become a function of the implied volatility surface.     

Switching interest rate sensitivity regimes of U.S. Corporates

We study interest rate sensitivities of U.S. investment grade BBB-rated and high yield corporate bonds over the period of 2001–2016. Our methodology assesses the capital gains of corporate bond portfolios and risk-free government bond portfolios, using average coupon and blended yield indices for the U.S. market. For both, U.S. BBB and high yield corporate bonds, we evidence the switching, from positive to negative interest rate sensitivity, occurring over the transition from the normal economic conditions to the periods of economic distress and vice-versa. The proposed theoretical explanation of such binary behavior posits an interrelation between interest rate and creditworthiness of issuers, which varies according to the phases of the business cycle. This research advances an economic understanding of interest rate risk management and sheds light on how financial institutions may develop strategies that hedge against downside risk.     

Monetary effects on nominal oil prices

The paper presents a theory of nominal asset prices for competitively owned oil. Focusing on monetary effects, with flexible oil prices the US dollar oil price should follow the aggregate US price level. But with rigid nominal oil prices, the nominal oil price jumps proportionally to nominal interest rate increases. We find evidence for structural breaks in the nominal oil price that are used to illustrate the theory of oil price jumps. The evidence also indicates strong Granger causality of the oil price by US inflation as is consistent with the theory.     

On the forecasting performance of a small-scale DSGE model

Dynamic stochastic general equilibrium (DSGE) models have recently become standard tools for policy analysis. Nevertheless, their forecasting properties have still barely been explored. In this article, we address this problem by examining the quality of forecasts of the key U.S. economic variables: the three-month Treasury bill yield, the GDP growth rate and GDP price index inflation, from a small-size DSGE model, trivariate vector autoregression (VAR) models and the Philadelphia Fed Survey of Professional Forecasters (SPF). The ex post forecast errors are evaluated on the basis of the data from the period 1994–2006. We apply the Philadelphia Fed “Real-Time Data Set for Macroeconomists” to ensure that the data used in estimating the DSGE and VAR models was comparable to the information available to the SPF.Overall, the results are mixed. When comparing the root mean squared errors for some forecast horizons, it appears that the DSGE model outperforms the other methods in forecasting the GDP growth rate. However, this characteristic turned out to be statistically insignificant. Most of the SPF's forecasts of GDP price index inflation and the short-term interest rate are better than those from the DSGE and VAR models.     

Short-term spot rate models with nonparametric deterministic drift

Most studies assume stationarity when testing continuous-time interest-rate models. However, consistent with Bierens [Bierens, H. (1997). Testing the unit root with drift hypothesis against nonlinear trend stationary, with an application to the US price level and interest rate. Journal of Econometrics, 81, 29–64; Bierens, H. (2000). Nonparametric nonlinear co-trending analysis, with an application to interest and inflation in the United States. Journal of Business and Economics Statistics, 18, 323–337], our nonparametric test results support nonlinear trend stationarity. To accommodate nonstationarity, we detrend the interest-rate series and re-examine a variety of continuous-time models. The goodness-of-fit improves significantly for those models with drift-induced mean reversion and worsens for those with high volatility elasticity. The inclusion of a nonparametric trend component in the drift significantly reduces the level effect on the interest-rate volatility. These results suggest that the misspecification of the constant elasticity model should be attributed to the nonlinear trend component of the short-term interest-rate process.     

Forecasting crude oil prices with DSGE models

In this study, we conducted an oil prices forecasting competition among a set of structural models, including vector autoregression and dynamic stochastic general equilibrium (DSGE) models. Our results highlight two principles. First, forecasts should exploit the fact that real oil prices are mean reverting over long horizons. Second, models should not replicate the high volatility of the oil prices observed in samples. By following these principles, we show that an oil sector DSGE model performs much better at real oil price forecasting than random walk or vector autoregression.     

A statistical identity linking folded and censored distributions

This paper models expected future values of Gaussian stochastic processes that are bounded by reflecting barriers. Such expectations are of course crucial to any model with forward looking agents. The approach is illustrated by applying it to an exchange rate target zone. By adopting a distributional approach, the formal analysis can be both simple and somewhat elegant. In doing so, we show that the first moments of folded and censored distributions are related in a surprisingly neat way. The setting is discrete-time, though where appropriate we extend the analysis to the continuous-time analogue of reflected Brownian motion.     

Investigating the PPP hypothesis using constructed U.S. dollar equilibrium exchange rate misalignments over the post-bretton woods period

This paper investigates the PPP-hypothesis over the post-Bretton Woods period using a representation of the equilibrium exchange rate (EER) that is an alternative to the real exchange rate. The results provide evidence in support of the relative-PPP hypothesis over the current period of floating exchange rates (1974–2005); while stronger evidence is found for the post-Plaza Accord period (1986–2005). EERs based on export price indexes (EPI) and constructed traded goods price indexes (TPI) best demonstrate the mean reverting behavior of the spot exchange rate as opposed to those EERs based on CPI, PPI, or the GDP-deflator. This mean reverting behavior is slightly improved if one takes international interest rate differentials into account; however EERs extended by productivity differentials do not indicate any improvements over the base model. Over the post-Plaza Accord period average half-lives of less than 1 year are reported using TPI-based EERs, adjusted by interest rate differentials. For large misalignments, we find probabilities that the spot exchange rate will converge towards the constructed CPI-based equilibrium exchange rate of up to 80%. Lastly, over the post-Plaza Accord period, the TPI-based EERs are able to statistically significantly outperform the pure random walk at short-term forecast horizons of less than 1 year for some spot exchange rates.     

London calling: Nonlinear mean reversion across national stock markets

This paper revisits empirical evidence of mean reversion of relative stock prices in international stock markets. We implement a strand of univariate and panel unit root tests for linear and nonlinear models of 18 national stock indices from 1969 to 2016. Our major findings are as follows. First, we find strong evidence of nonlinear mean reversion of the relative stock price with the UK index as the reference, calling attention to the stock index in the UK, but not with the US index. Our results imply an important role of the local common factor in the European stock markets. Second, panel tests yield no evidence of linear and nonlinear stationarity when the cross-section dependence is considered, which provides conflicting results from those of the univariate tests. Last, we show how to understand these results via dynamic factor analysis. When the stationary common factor dominates nonstationary idiosyncratic components in small samples, panel tests that filter out the stationary common factor may yield evidence against the stationarity null hypothesis in finite samples. We corroborate this conjecture via extensive Monte Carlo simulations.     

Macroeconomic responses of emerging market economies to oil price shocks: An analysis by region and resource profile

We analyze the impact of oil price shocks on the macroeconomic fundamentals in emerging economies in three regions that have different resource endowments. The existing literature on emerging economies remains inconclusive on how regional factors and resource characteristics affect the response of macroeconomic variables to oil price shocks. We show that (1) exports in Europe and Central Asia are driven by oil more than East Asia and the Pacific and that (2) policy makers in East Asia and the Pacific should be concerned about real exchange appreciation following a positive oil shock to mitigate losses in the non-oil export market. Analysis by resource endowment further reveals that, in less-resource-intensive economies, an oil price shock causes large variations in consumption and has a negative and persistent impact on the real gross domestic product (GDP). In mineral-exporting economies, real GDP and interest rates are driven largely by oil price shocks. The response of real GDP in mineral-exporting economies is short lived. In oil-exporting economies, only real GDP has a large variation in response to oil price shocks. Our findings highlight the need for customized policy responses to oil price shocks, depending on resource endowments, as we show that a “one size fits all" policy does not exist.     

A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuous-time components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easy-to-implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and Lévy-driven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the high-frequency intraday data.     

Generalized spectral testing for multivariate continuous-time models

We develop an omnibus specification test for multivariate continuous-time models using the conditional characteristic function, which often has a convenient closed-form or can be accurately approximated for many multivariate continuous-time models in finance and economics. The proposed test fully exploits the information in the joint conditional distribution of underlying economic processes and hence is expected to have good power in a multivariate context. A class of easy-to-interpret diagnostic procedures is supplemented to gauge possible sources of model misspecification. Our tests are also applicable to discrete-time distribution models. Simulation studies show that the tests provide reliable inference in finite samples.     

The impact of inflationary news on money market yields and volatilities

This study investigates the impact of surprises in hourly wages, non-farm payroll, unemployment rate, and producer price index on the yields and volatilities of money market securities. The methodology is conducted in a framework that preserves the strong substitutability among the instruments. We find first the short-term interest rate nexus is inherently a steady state long-run phenomenon. Second, yield variability is fundamentally linked to the release of macroeconomic news that conveys important information on inflation. Third, results from the equality of variance tests suggest that volatilities on announcement days are significantly higher than non-announcement day volatilities across all securities.     

The effect of systematic risk factors on counterparty default and credit risk of interest rate swaps

This research investigates the effect of specific systematic risk factors on credit risk pricing and capital allocation of interest rate swaps. Because of the stochastic nature of uncertain future cash flows and interest rates, practitioners typically employ the Black-Scholes option pricing model in combination with a simulation analysis to establish capital requirements and estimate the shadow price of an interest rate swap. However, this practice of pricing swap risk excludes systematic risk factors that affect the risk shadow price, thereby underestimating the capital allocation required for financial institutions. This research demonstrates the effect of risk mispricing when simulation models ignore systematic risk factors such as model risk, convexity risk, and parameter risk on the pricing of interest rate swaps.