Inequality Constraints in the Fractionally Integrated GARCH Model

In this article we derive necessary and sufficient conditionsfor the nonnegativity of the conditional variance in the fractionallyintegrated generalized autoregressive conditional heteroskedastic(p, d, q) (FIGARCH) model of the order p 2 and sufficient conditionsfor the general model. These conditions can be seen as beinganalogous to those derived by Nelson and Cao (1992, Journalof Business & Economic Statistics 10, 229–235) forthe GARCH(p, q) model. However, the inequality constraints whichwe derive for the FIGARCH model illustrate two remarkable propertiesof the FIGARCH model which are in contrast to the GARCH model:(i) even if all parameters are nonnegative, the conditionalvariance can become negative and (ii) even if all parametersare negative (apart from d), the conditional variance can benonnegative almost surely. In particular, the conditions forthe (1, d, 1) model substantially enlarge the sufficient parameterset provided by Bollerslev and Mikkelsen (1996, Journal of Econometrics73, 151–184). The importance of the result is illustratedin an empirical application of the FIGARCH(1, d, 1) model toJapanese yen versus U.S. dollar exchange rate data.     

Practitioners' Corner

The first 150 words of the full text of this article appear below. The transition from some preliminary qualitative assessmentsto quantitative assertions is a hallmark of scientific progress.One dollar today is more valuable than one dollar availabletomorrow, but the scientific issue is by how much and why thisamount? Similarly a random gain with unit expectation and significantrisk is less valuable than one dollar available with certainty.Financial theories of the discount rate and the mean-variancetrade-off have afforded helpful quantitative answers to thesecrucial issues in asset pricing, investment, and risk management.Meanwhile, modern financial econometrics has characterized thedynamic features of interest rates as well as of risk and returnthrough state variables models with volatility clustering, mean-volatilityfeedback, and dynamic correlations. From this perspective, a striking common feature of all thearticles in the current issue of the Journal of Financial Econometricsis the reintroduction of qualitative variables previously treatedusing purely quantitative approaches. The first . . . [Full Text of this Article]     

Government intervention and adverse selection costs in foreign exchange markets

An important group of traders in the foreign exchange marketis governments who often adhere to a foreign exchange rate policyof occasional interventions with otherwise floating rates. Inthis article we provide a theoretical model and empirical evidencethat government foreign exchange interventions create significantadverse selection problems for dealers. In particular, our modelshows that the adverse selection component of the foreign exchangespread is positively related to the variance of unexpected interventionand that expected intervention has no impact on the spread.After controlling for inventory and order processing costs,we find that bid-ask spreads increase with U.S. dollar and Germandeutsche mark foreign exchange rate intervention during theperiod 1976-1994. Furthermore, when the intervention is decomposedinto expected and unexpected components, we find a statisticallyand economically significant increase in spreads with the varianceof unexpected intervention, while expected intervention hasno significant impact on spreads.     

Explaining and forecasting the euro/dollar exchange rate through a non-linear threshold model

A linear econometric error correction model (ECM) model is built, based on short interest rates, gross domestic product (GDP) growth expectations and inflation differentials, in order to explain the euro/dollar exchange rate dynamics and provide reliable forecasts. This specification performs well. However, the introduction of non-linear threshold dynamics provides a better understanding of ‘abnormal’ features other than deviations from long-run equilibrium levels, allowing for the possibility of asymmetric behaviour. Empirical evidence of this is found in the actual dynamics of the euro. The non-linear specification performs better than the linear model in both in-sample fitting and out-of-sample forecasting, showing that fundamentals hold, working also through some non-linear mechanism, in explaining the euro/dollar dynamics.     

Dynamic conditional copula correlation and optimal hedge ratios with currency futures

This study investigates efficiency of the futures hedge implemented through the currency markets. The copula DCC-EGARCH model is estimated with the bivariate error correction term to minimize variance of the currency portfolios. The estimation results for the currencies of the Australian dollar, Canadian dollar, euro, British pound and Japanese yen show that the inclusion of the external realized variance estimators into the variance equation of the estimated model improves the model's ability to account for the clustered data variance. In hedging portfolios, the information content of the realized variance estimator effectively reduces the variance of the portfolios.     

Change in Volatility in the Won/U.S. Dollar Daily Exchange Rate:Stochastic Volatility Model

This study estimates the changes in volatility of the won/U.S. dollar dailyexchange rates before and after the Korean currency crisis, using the stochastic volatility model with the ARMAregression error term. We find that the persistence of volatility increased after the Koreancurrency crisis.     

LARCH, Leverage, and Long Memory

We consider the long-memory and leverage properties of a modelfor the conditional variance of an observable stationary sequence X_t, where is the square of an inhomogeneous linear combination of X_s, s < t, withsquare summable weights b_j. This model, which we call linearautoregressive conditionally heteroskedastic (LARCH), specializes,when depends only on X_t–1, to theasymmetric ARCH model of Engle (1990, Review of Financial Studies3, 103–106), and, when depends only on finitely many X_s, to a version of the quadratic ARCH modelof Sentana (1995, Review of Economic Studies 62, 639–661),these authors having discussed leverage potential in such models.The model that we consider was suggested by Robinson (1991,Journal of Econometrics 47, 67–84), for use as a possiblylong-memory conditionally heteroskedastic alternative to i.i.d.behavior, and further studied by Giraitis, Robinson and Surgailis(2000, Annals of Applied Probability 10, 1002–1004), whoshowed that integer powers , =" BORDER="0">2 can have long-memory autocorrelations. We establish conditionsunder which the cross-autocovariance function between volatilityand levels, , decays in the manner of moving average weights of long-memory processes on suitable choiceof the b_j. We also establish the leverage property that h_t <0 for 0 < t k, where the value of k (which may be infinite)again depends on the b_j. Conditions for finiteness of thirdand higher moments of X_t are also established.     

A closed-form GARCH option valuation model

This paper develops a closed-form option valuation formula fora spot asset whose variance follows a GARCH(p, q) process thatcan be correlated with the returns of the spot asset. It providesthe first readily computed option formula for a random volatilitymodel that can be estimated and implemented solely on the basisof observables. The single lag version of this model containsHeston's (1993) stochastic volatility model as a continuous-timelimit. Empirical analysis on S&P500 index options showsthat the out-of-sample valuation errors from the single lagversion of the GARCH model are substantially lower than thead hoc Black-Scholes model of Dumas, Fleming and Whaley (1998)that uses a separate implied volatility for each option to fitto the smirk/smile in implied volatilities. The GARCH modelremains superior even though the parameters of the GARCH modelare held constant and volatility is filtered from the historyof asset prices while the ad hoc Black-Scholes model is updatedevery period. The improvement is largely due to the abilityof the GARCH model to simultaneously capture the correlationof volatility, with spot returns and the path dependence involatility.     

Spin-offs, Divestitures, and Conglomerate Investment

We examine whether spin-offs or divestitures cause improvementsin conglomerate investment efficiency. At issue are endogeneityof these restructuring decisions and correct measurement ofinvestment efficiency. Endogeneity is a problem because thefactors that induce firms to spin off or divest divisions mayalso improve investment efficiency; measurement error is a problembecause efficiency measures employ Tobin’s q as a noisyproxy for investment opportunities. We find important differencesbetween firms that divest or spin off and a control sample.After accounting for these differences and for measurement errorin q, we find no evidence of improvements in investment efficiency.(JEL G31, G34)     

Order Flow and the Monetary Model of Exchange Rates: Evidence from a Novel Data Set

We propose an exchange rate model that is a hybrid of the conventional specification with monetary fundamentals and the Evans–Lyons microstructure approach. We estimate a model augmented with order flow variables, using a unique data set: almost 100 monthly observations on interdealer order flow on dollar/euro and dollar/yen. The augmented macroeconomic, or “hybrid,” model exhibits greater in‐sample stability and out of sample forecasting improvement vis‐à‐vis the basic macroeconomic and random walk specifications.     

Auditor Expertise and the Estimation of Dollar Error in Accounts

A major task that auditors undertake in formulating their audit opinion is to estimate the dollar error that might exist in accounts in light of their evaluation of internal control strengths and weaknesses. The research that has been undertaken to evaluate the quality of auditor performance on this task, however, has produced mixed results. The current study tries to overcome some theoretical limitations and measurement limitations that have undermined prior studies. Forty practising auditors rated their abilities on fourteen characteristics derived from a model of expertise. They then undertook an experiment where they judged the extent of dollar error that might exist in the inventories of a manufacturing company. They based their judgments on working papers provided to them that contained, among other information, an evaluation of the company's internal control system. An estimate of the 'true' dollar error in the inventories was calculated using a program that simulated the company's internal control and accounting system. This estimate was then used to calculate the accuracy of the auditors' judgments. Their ratings on the expertise characteristics were not related to their judgment accuracy. Their ratings were related, however, to their confidence in their judgment accuracy. Auditors who considered themselves more expert at the task were more confident in their judgment accuracy but they were, in fact, no more accurate than auditors who considered themselves to be less expert at the task.     

Pricing Interest Rate Derivatives: A General Approach

The relationship between affine stochastic processes and bondpricing equations in exponential term structure models has beenwell established. We connect this result to the pricing of interestrate derivatives. If the term structure model is exponentialaffine, then there is a linkage between the bond pricing solutionand the prices of many widely traded interest rate derivativesecurities. Our results apply to m-factor processes with n diffusionsand l jump processes. The pricing solutions require at mosta single numerical integral, making the model easy to implement.We discuss many options that yield solutions using the methodsof the article.     

Official interventions and the forward premium anomaly

This paper presents evidence that the forward premium anomaly intensifies during those times when a central bank intervenes. A model of exchange rate determination is presented to explain this and other features of the dollar–deutschemark and dollar–yen markets. In the model, the forward premium anomaly is caused by surprise central bank interventions in the foreign exchange market. Because interventions are pure surprises, the violations of uncovered interest parity that they create do not represent ex ante profit opportunities. Simulations of the model are found to match the forward premium anomaly and several other notable features of the data. The model also provides a theoretical basis for ARCH effects in exchange-rate returns.     

The Book-to-Market and Size Effects in a General Asset Pricing Model: Evidence from Seven National Markets

The positive relation of returns with Book-to-Market ratio (BE/ME)and their negative relation withMarket Value(MVE) remains strongunder a general stochastic discount function (SDF) that doesnot depend on a specific asset pricing model and avoids potentiallyserious simultaneity biases inherent in the Fama and Frenchthree-factor model. However, we find that SDF_s that includethe equivalent of the HML portfolio do not span all asset sub-spaces,even with additional conditioning information. Finally, macroand financial variables we introduce to the pricing functionsdo not offer an alternative explanation of the BE/ME effect.JEL Classification codes: G10, G12, G15, G30.     

Higher Moments and Exchange Rate Behavior

This paper uses 15‐minute exchange rate returns data for the six most liquid currencies (i.e., the Australian dollar, British pound, Canadian dollar, Euro, Japanese yen, and Swiss franc) vis‐à‐vis the United States dollar to examine whether a GARCH model augmented with higher moments (HM‐GARCH) performs better than a traditional GARCH (TG) model. Two findings are unraveled. First, the inclusion of odd/even moments in modeling the return/variance improves the statistical performance of the HM‐GARCH model. Second, trading strategies that extract buy and sell trading signals based on exchange rate forecasts from HM‐GARCH models are more profitable than those that depend on TG models.     

Frequency of observation and the estimation of integrated volatility in deep and liquid financial markets

Using two newly available ultrahigh-frequency datasets, we investigate empirically how frequently one can sample certain foreign exchange and U.S. Treasury security returns without contaminating estimates of their integrated volatility with market microstructure noise. Using the standard realized volatility estimator, we find that one can sample dollar/euro returns as frequently as once every 15 to 20 s without contaminating estimates of integrated volatility; 10-year Treasury note returns may be sampled as frequently as once every 2 to 3 min on days without U.S. macroeconomic announcements, and as frequently as once every 40 s on announcement days. Using a simple realized kernel estimator, this sampling frequency can be increased to once every 2 to 5 s for dollar/euro returns and to about once every 30 to 40 s for T-note returns. These sampling frequencies, especially in the case of dollar/euro returns, are much higher than those that are generally recommended in the empirical literature on realized volatility in equity markets. The higher sampling frequencies for dollar/euro and T-note returns likely reflect the superior depth and liquidity of these markets.     

Practitioners' Corner

The first 150 words of the full text of this article appear below. In our discussion in the last issue of Journal of FinancialEconometrics (JFEC) of the nonparametric methods developed byBarndorff-Nielsen and Shephard (2006) to detect jumps in thelocal behavior of the continuous time path of a price process,we observed these tests were not designed to detect major pricediscontinuity events such as the 1987 crash, since the testingmethodology precludes jumps in adjacent time intervals. Indeed,a major event such as Black Monday is characterized by a sequenceof jumps in consecutive time intervals throughout the day. Inthe interest of thematic continuity, let’s pursue thematter of jumps further. The first article in the current issue by Hossein Asgharianand Chistoffer Bengtsson addresses directly the detection ofbig events in stock prices. More particularly, the authors analyzethe spillover of jumps across international stock markets. Tomeasure jumps, the authors formulate a parametric model in . . . [Full Text of this Article]     

When and how US dollar shortages evolved into the full crisis? Evidence from the cross-currency swap market

This paper investigates when and how the US dollar shortages evolved into the full crisis in the cross-currency swap market between major European currencies and the US dollar during the turmoil of 2007-2009, using the dynamic factor model with regime-switching β coefficients of each swap price with respect to the latent common factor. The 1-year market entered the high-β crisis regime soon after the onset of the subprime problem in August 2007. The 10-year market entered that regime following the collapse of Bear Sterns in mid-March 2008. Financial credit spreads have significant predictive power for switches between high and low-β regimes.     

Macroeconomic Factors Do Influence Aggregate Stock Returns

Stock market returns are significantly correlated with inflationand money growth. The impact of real macroeconomic variableson aggregate equity returns has been difficult to establish,perhaps because their effects are neither linear nor time invariant.We estimate a GARCH model of daily equity returns, where realizedreturns and their conditional volatility depend on 17 macroseries' announcements. We find six candidates for priced factors:three nominal (CPI, PPI, and a Monetary Aggregate) and threereal (Balance of Trade, Employment Report, and Housing Starts).Popular measures of overall economic activity, such as IndustrialProduction or GNP are not represented.     

The Stochastic Properties of Major Canadian Exchange Rates

This paper extends the results of Akgiray and Booth [2] on the stochastic properties of five major Canadian exchange rates using the EGARCH-M model along with the generalized error distribution (GED). In addition to the issue of first- and second-order dependencies, explored by the authors, the paper (1) addresses the issue of asymmetric volatility, (2) examines the extent to which volatility affects future movements in these exchange rates, (3) measures the amount of kurtosis in the data, and (4) investigates the transmission mechanism of innovations and volatility shocks across the five Canadian exchange rate markets. The five Canadian dollar exchange rates are for the U.S. dollar, the Japanese yen, the British pound, the German mark, and the French franc. Changes in Canadian exchange rates are conditionally heteroskedastic, a finding which is in line with that of Akgiray and Booth [2]. There is no evidence supporting the assertion that volatility triggers such changes. The hypothesis of asymmetric volatility is rejected for all Canadian exchange rates; thus unexpected appreciations and depreciations of the Canadian currency have similar impact on future volatility of these exchange rates. Innovations in the Canadian exchange rate markets for the U.S. dollar, the British pound, and French franc influence the Japanese yen market, while innovations in the markets of the British pound and German mark influence the French franc market. Significant but negative volatility spillovers radiate from the German mark market to the U.S. dollar market and from the French franc market to the German mark market, resulting in lower levels of volatility in both the U.S. and German markets. The distributions of all five series of Canadian exchange rates are highly leptokurtic relative to the normal distribution. The GED distribution provides a good characterization of these distributions.