Unbiasedness of the Forward Exchange Rates

This paper derives an error correction model under the assumption that the spot and the forward rates are cointegrated, the first difference of forward rates is stationary, and the first order autocorrelation in the forecast error is allowed. When tests of the unbiasedness hypothesis are conducted with an error correction model using generalized methods of moments [GMM], the unbiasedness hypothesis cannot be rejected. Furthermore, the multivariate GMM estimation supports the hypothesis of unbiasedness of the forward exchange rates and the absence of a risk premium in the foreign exchange markets.     

Can exchange rate volatility explain persistence in the forward premium?

The persistence of the forward premium has been cited both as evidence of the failure of the unbiasedness hypothesis and as rationale for the forward premium anomaly. This paper examines the recent proposition that forward premium persistence can be explained solely by the conditional variance of the spot rate. We provide theoretical and empirical evidence to challenge this proposition. Our empirical results are shown to be robust to the presence of structural breaks. A corollary of the results is that the ‘true’ risk premium contains a long memory component. This is non-standard and has implications for the construction of rational expectations models of the foreign exchange market.     

Efficiency tests with overlapping data: an application to the currency options market

This paper presents the results of an empirical study into the efficiency of the currency options market. The methodology derives from a simple model often applied to the spot and forward markets for foreign exchange. It relates the historic volatility of the underlying asset to the implied volatility of an option on the underlying at a specified prior time and then proceeds to test obvious hypotheses about the values of the coefficients. The study uses panel regression to address the problem of overlapping data which leads to dependence between observations. It also uses volatility data directly quoted on the market in order to avoid the biases which may occur when ‘backing out’ volatility from specific option pricing models. In general, the evidence rejects the hypothesis that the currency option market is efficient. This suggests that implied volatility is not the best predictor of future exchange rate volatility and should not be used without modification: the models presented in this paper could be a way of producing revised forecasts.     

Forecasting implied volatility in foreign exchange markets: a functional time series approach

We utilise novel functional time series (FTS) techniques to characterise and forecast implied volatility in foreign exchange markets. In particular, we examine the daily implied volatility curves of FX options, namely; Euro/United States Dollar, Euro/British Pound, and Euro/Japanese Yen. The FTS model is shown to produce both realistic and plausible implied volatility shapes that closely match empirical data during the volatile 2006–2013 period. Furthermore, the FTS model significantly outperforms implied volatility forecasts produced by traditionally employed parametric models. The evaluation is performed under both in-sample and out-of-sample testing frameworks with our findings shown to be robust across various currencies, moneyness segments, contract maturities, forecasting horizons, and out-of-sample window lengths. The economic significance of the results is highlighted through the implementation of a simple trading strategy.     

Forward exchange market unbiasedness: the case of the Australian dollar since 1984

This paper implements a robust statistical approach to regression with non-stationary time series. The methods were recently developed in other work and are briefly exposited here. They allow us to perform regressions in levels with non-stationary time series data, they accommodate data distributions with heavy tails and they permit serial dependence and temporal heterogeneity of unknown form in the equation errors. With these features the methods are well suited to applications with frequently sampled exchange rate data, which generally display all of these empirical characteristics. Our application here is to daily data on spot and forward exchange rates between the Australian and US dollars over the period 1984–1991, following the deregulation of the Australian foreign exchange market. We find big differences between the robust and the non-robust regression outcomes and in the associated statistical tests of the hypothesis that the forward rate is an unbiased predictor of the future spot rate. The robust tests reject the unbiasedness hypothesis but still give the forward rate an important role as a predictor of the future spot rate.     

Foreign exchange,fractional cointegration and the implied–realized volatility relation

Almost all relevant literature has characterized implied volatility as a biased predictor of realized volatility. In this paper we provide new time series techniques to investigate the validity of this finding in several foreign exchange options markets, including the Euro market. First, we develop a new fractional cointegration test that is shown to be robust to both stationary and non-stationary regions. Second, we employ both intra-day and daily data to measure realized volatility in order to assess the relevance of data frequency in resolving the bias. Third, we use data on implied volatility traded on the market. In contrast to previous studies, we show that the frequency of data used for measuring realized volatility within a fractionally cointegrating framework is important for the results of unbiasedness tests. Significantly, for many popular exchange rates, the use of intra-day rather than daily data affects the emergence of a different bias, as the possibility of a fractionally integrated risk premium admits itself!     

An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for pricing currency options based on a third order asymptotic expansion scheme; we do not model a foreign exchange rate’s variance such as in Heston [(1993) The Review of Financial studies, 6, 327–343], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. Finally, numerical examples are provided and the pricing formula are applied to the calibration of volatility surfaces in the JPY/USD option market.     

Do fear indices help predict stock returns?

This study investigates the forecasting power of implied volatility indices on forward looking returns. Prior studies document that negative innovations to returns are associated with increasing implied volatility of the underlying indices; thus, suggesting a possible relationship between extremely high levels of implied volatility and positive short term returns. We investigate this issue by examining the predictive power of three implied volatility indices, VIX, VXN and VDAX, on the underlying index returns. We extend previous research by also focusing on characterised selected stocks and examine the relationship between implied volatility indices and future returns across different sectors and classified portfolios. Our findings suggest that implied volatility indices are good predictors of 20-days and 60-days forward looking returns and illustrate insignificant predictive power for very short term (1-day and 5-days) returns.     

The forward rate unbiasedness hypothesis reexamined: evidence from a new test

Under conditions of risk neutrality and rational expectations in the foreign exchange market, there should be a one-to-one relationship between the forward rate and the corresponding future spot rate. However, cointegration-based tests of the unbiasedness hypothesis of the forward rate have produced mixed findings. In order to exploit significant cross-sectional dependencies, we test the unbiasedness hypothesis using a new multivariate (panel) unit-root test, the Johansen likelihood ratio (JLR) test, which offers important methodological advantages over alternative standard panel unit-root tests. When applied to a data set of eight major currencies in the post-Bretton Woods era, the JLR test provides strong and robust evidence in support of a unitary cointegrating vector between forward and corresponding future spot rates. However, the orthogonality condition is satisfied only for three major currencies.     

The Unbiasedness Hypothesis in the Freight Forward Market: Evidence from Cointegration Tests

The current paper investigates the unbiasedness hypothesis of Forward Freight Agreement (FFA) prices in the freight over-the-counter (OTC) forward market trades. Cointegration techniques are employed to examine the hypothesis. The results indicate that: FFA prices one and two months before maturity are unbiased predictors of the realised spot freight rates for all investigated shipping routes; three months FFA prices for panamax Pacific routes are unbiased predictors of spot prices, while FFA prices for panamax Atlantic routes are found to be biased predictors of spot prices. This diverse evidence suggests that the validity of the unbiasedness hypothesis depends on the specific characteristics of the market under investigation, the selected trading route and the time to maturity of the contract. JEL classification G13, G14, C32     

Reducing reporting risk: Designating foreign currency forward contracts as cash flow hedges

We present an example that compares the effects on earnings of designating a foreign currency forward contract as either a cash-flow or fair-value hedge of a foreign currency denominated receivable. Entities engaging in exchange transactions not denominated in their functional currency frequently enter into foreign currency forward contracts in order to mitigate their foreign exchange rate risk exposure. The aggregate effect on earnings of the transaction gain or loss on the foreign currency receivable and the gain or loss on the forward contract is known on the date the forward contract is initiated. The effect on each period’s earnings during the term of a forward contract designated as a cash-flow hedge is also known on the date the contract is initiated; whereas the effect on each periods’ earnings from a fair-value hedge cannot be determined until the respective balance sheet dates. Therefore, designating forward contracts as cash-flow hedges may suppress volatility in reported earnings compared to designating forward contracts as fair-value hedges. In addition, the reporting risk (the amount of uncertainty surrounding the pending measure of an item to be reported in the financial statements) is lower when a forward contract is designated as a cash-flow hedge relative to designating it as a fair-value hedge. This suggests foreign currency forward contracts designated as cash-flow hedges are more consistent with the purpose of hedge accounting: to mitigate the effects on earnings of applying different measurement criteria for the hedge and the hedged item.     

Expectations Hypothesis of the Term Structure of Implied Volatility: Evidence from Foreign Currency and Stock Index Options

Using a stochastic volatility option pricing model, we showthat the implied volatilities of at-the-money options are notnecessarily unbiased and that the fixed interval time-seriescan produce misleading results. Our results do not support theexpectations hypothesis: long-term volatilities rise relativeto short-term volatilities, but the increases are not matchedas predicted by the expectations hypothesis. In addition, anincrease in the current long-term volatility relative to thecurrent short-term volatility is followed by a subsequent decline.The results are similar for both foreign currency and the S&P500 stock index options.     

Coupling smiles

The present paper addresses the problem of computing implied volatilities of options written on a domestic asset based on implied volatilities of options on the same asset expressed in a foreign currency and the exchange rate. It proposes an original method together with explicit formulae to compute the at-the-money implied volatility, the smile's skew, convexity, and term structure for short maturities. The method is completely free of any model specification or Markov assumption; it only assumes that jumps are not present. We also investigate how the method performs on the particular example of the currency triplet dollar, euro, yen. We find a very satisfactory agreement between our formulae and the market at one week and one month maturities.     

Central Bank Intervention in USD/INR Market: Estimating Its Reaction Function and Impact on Volatility

Econometric evidence on why central banks intervene in the foreign exchange market and the impact of such intervention has remained inconclusive. We contribute to the literature with evidence from India, a managed float regime that sees consistent monitoring and intervention by Reserve Bank of India, India’s central bank. Estimation of the central bank reaction function shows that increased volatility in the foreign exchange market and misalignment from targeted rates are important objectives behind intervention. The paper further uses the GARCH framework to study how intervention influences exchange rate volatility. We find that intervention in the spot market increases volatility while that in the forward market reduces volatility.     

Testing the unbiasedness hypothesis in the forward foreign exchange market: A specification analysis

This paper evaluates two popular regression methods of testing the unbiasedness hypothesis in the forward foreign exchange market. For the 30-day Canada/United States forward foreign exchange market, the evidence overwhelmingly indicates that it is inappropriate to treat the structure of the systematic and stochastic components of the test relations as constant over time. Hence, conclusions inferred from parameter significance testing based upon full-sample estimation can be very misleading. Accordingly, we argue for a specification analysis of the test relations, and more explicit modelling of market fundamentals.     

New evidence on the implied-realized volatility relation

We consider the relation between the volatility implied in an option's price and the subsequently realized volatility. Earlier studies on stock index options have found biases and inefficiencies in implied volatility as a forecast of future volatility. More recently, Christensen and Prabhala find that implied volatility in at-the-money one-month OEX call options on the S&P 100 index in fact is an unbiased and efficient forecast of ex-post realized index volatility after the 1987 stock market crash. In this paper, the robustness of the unbiasedness and efficiency result is extended to a more recent period covering April 1993 to February 1997. As a new contribution, implied volatility is constructed as a trade weighted average of implied volatilities from both in-the-money and out-of-the-money options and both puts and calls. We run a horse race between implied call, implied put, and historical return volatility. Several robustness checks, including a new simultaneous equation approach, underscore our conclusion, that implied volatility is an efficient forecast of realized return volatility.     

From implied to spot volatilities

This paper is concerned with the relation between spot and implied volatilities. The main result is the derivation of a new equation which gives the dynamics of the spot volatility in terms of the shape and the dynamics of the implied volatility surface. This equation is a consequence of no-arbitrage constraints on the implied volatility surface right before expiry. We first observe that the spot volatility can be recovered from the limit, as the expiry tends to zero, of at-the-money implied volatilities. Then, we derive the semimartingale decomposition of implied volatilities at any expiry and strike from the no-arbitrage condition. Finally the spot volatility dynamics is found by performing an asymptotic analysis of these dynamics as the expiry tends to zero. As a consequence of this equation, we give general formulas to compute the shape of the implied volatility surface around the at-the-money strike and for short expiries in general spot volatility models.     

FX volatility forecasts and the informational content of market data for volatility

The paper examines the medium-term forecasting ability of several alternative models of currency volatility. The data period covers more than eight years of daily observations, January 1991 to March 1999, for the spot exchange rate, 1- and 3-month volatility of the DEM/JPY, GBP/DEM, GBP/USD, USD/CHF, USD/DEM and USD/JPY. Comparing with the results of ‘pure’ time series models, the reported work investigates whether market implied volatility data can add value in terms of medium-term forecasting accuracy. This is done using data directly available from the marketplace in order to avoid the potential biases arising from ‘backing out’ volatility from a specific option pricing model. On the basis of the over 34 000 out-of-sample forecasts produced, evidence tends to indicate that, although no single volatility model emerges as an overall winner in terms of forecasting accuracy, the ‘mixed’ models incorporating market data for currency volatility perform best most of the time.     

Dynamics of foreign exchange implied volatility and implied correlation surfaces

The prices of currency options expressed in terms of their implied volatilities and the implied correlations between foreign exchange rates at a given point in time depend on option delta and time to maturity. Implied volatilities and implied correlations likewise may thus be represented as a surface. It is well known that these surfaces exhibit both skew/smile features and term structure effects and their shapes fluctuate substantially over time. Using implied volatilities on three currency pairs as well as historical implied correlation values between them, we study the nature of these fluctuations by applying a Karhunen-Loève decomposition that is a generalization of a principal component analysis. We demonstrate that the largest share in the dynamics of these surfaces' fluctuations may be explained by exactly the same three factors, providing evidence of strong interdependences between implied correlation and implied volatility of global currency pairs.     

Expectations,exchange rates and monetary theory: The case of German hyperinflation

This paper tests some of the structural coefficient restrictions on goods-price equations and foreign exchange-rate equations implied by the monetary theory of exchange rates. The data are from the German hyperinflation (1922–1923). The results of the tests broadly support the monetary theory of exchange rates and they also support the hypothesis that the foreign exchange market was efficient during this period. However, the much higher residual volatility in foreign exchange prices is not explained by the monetary theory.