International Capital Markets and Foreign Exchange Risk

Relations between foreign exchange risk premia, exchange ratevolatility, and the volatilities of the pricing kernels forthe underlying currencies, are derived under the assumptionof integrated capital markets. As predicted, the volatilityof exchange rates is significantly associated with the estimatedvolatility of the relevant pricing kernels, and foreign exchangerisk premia are significantly related to both the estimatedvolatility of the pricing kernels and the volatility of exchangerates. The estimated foreign exchange risk premia mostly satisfyFama’s (1984) necessary conditions for explaining theforward premium puzzle, but the puzzle remains in several caseseven after taking account of the pricing kernel volatilities.     

Arbitrage-free market models for option prices: the multi-strike case

This paper studies modeling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for constructing such models, we introduce the new concepts of local implied volatilities and price level. We show that these new quantities provide a natural and simple parametrization of all option price models satisfying the natural static arbitrage bounds across strikes. We next characterize absence of dynamic arbitrage for such models in terms of drift restrictions on the model coefficients. For the resulting infinite system of SDEs for the price level and all local implied volatilities, we then study the question of solvability and provide sufficient conditions for existence and uniqueness of a solution. We give explicit examples of volatility coefficients satisfying the required assumptions, and hence of arbitrage-free multi-strike market models of option prices.      

Equilibrium Exchange Rate Hedging

We assume a world like the one that gives the capital asset pricing model, but with many goods and many countries. We assume that investors in a given country have homothetic utility functions with the same weights, and a currency that has a sure end-of-period value using a price index with those weights. Siegel's paradox (derived from Jensen's inequality) makes investors want a positive amount of exchange risk. When average risk tolerance is the same across countries, every investor will hold the same mix of market risk (through the world market portfolio of all assets) and exchange risk (in a diversified basket of foreign currencies). In fact, the ratio of exchange risk to market risk is equal to the average investor's risk tolerance. We can write the ratio of exchange risk to market risk (and the fraction of the market's exchange risk that investors hedge) as depending on an average of world market risk premia, an average of world market volatilities, and an average of exchange rate volatilities. The weights in these averages are the same as the weights of the different countries in the currency basket. Given these averages, the ratio (and the fraction hedged) will not depend directly on exchange rate means or covariances. In equilibrium, we can use the ratio of exchange risk to market risk to measure average risk tolerance: in this model, risk tolerance is observable.     

Exchange Rates and the Conversion of Currency‐Specific Risk Premia

How do the risk factors that drive asset prices influence exchange rates? Are the parameters of asset price processes relevant for specifying exchange rate processes? Most international asset pricing models focus on the analysis of asset returns given exchange rate processes. Little work has been done on the analysis of exchange rates dependent on asset returns. This paper uses an international stochastic discount factor (SDF) framework to analyse the interplay between asset prices and exchange rates. So far, this approach has only been implemented in international term structure models. We find that exchange rates serve to convert currency‐specific discount factors and currency‐specific prices of risk – a result linked to the international arbitrage pricing theory (IAPT). Our empirical investigation of exchange rates and stock markets of four countries presents evidence for the conversion of currency‐specific risk premia by exchange rates.     

Information in the Term Structure of Yield Curve Volatility

Using a novel no‐arbitrage model and extensive second‐moment data, we decompose conditional volatility of U.S. Treasury yields into volatilities of short‐rate expectations and term premia. Short‐rate expectations become more volatile than premia before recessions and during asset market distress. Correlation between shocks to premia and shocks to short‐rate expectations is close to zero on average and varies with the monetary policy stance. While Treasuries are nearly unexposed to variance shocks, investors pay a premium for hedging variance risk with derivatives. We illustrate the dynamics of the yield volatility components during and after the financial crisis.     

Implied volatility linkages among major European currencies

This paper examines linkages in expected future volatilities among major European currencies. For that purpose, volatility expectations implied by currency options on the euro, British pound, and Swiss franc quoted against the U.S. dollar are analysed. Vector autoregressive modelling is applied to ascertain the dynamics of the implied volatilities across currencies. The results show that the market expectations of future exchange rate volatilities are closely linked among major European currencies. Furthermore, it is found that the implied volatility of the euro significantly affects the volatility expectations of the British pound and the Swiss franc.     

The determinants of the model-free positive and negative volatilities

In this paper we analyze the role of macroeconomic and financial determinants in explaining stock market volatilities in the U.S. market. Both implied and realized volatility are computed model-free and decomposed into positive and negative components, thereby allowing us to compute directional volatility risk premia. We capture the behaviour of each component of implied volatility and risk premium in relation to their different determinants. The negative implied volatility appears to be linked more towards financial conditions variables such as uncertainty and geopolitical risk indexes, whereas positive implied volatility is driven more by macro variables such as inflation and GDP. There is a clear shift in importance from macro towards financial determinants moving from the pre towards the post financial crisis. A mixed frequency Granger causality approach uncovers causality relationships between volatilities and risk premia and macro variables and vice versa, a finding which is not detected with a conventional low frequency VAR model.     

THE VALUATION OF CURRENCY OPTIONS FOR ALTERNATE STOCHASTIC PROCESSES

This paper compares the ability of four valuation models — the Pure Diffusion model of Black-Scholes-Merton, the Absolute Diffusion and Pure Jump models of Cox-Ross, and the mixed Jump-Diffusion model of Merton — to explain the observed behavior of market prices of foreign currency options. The empirical tests are based on a comparison of the pattern of implied volatilities obtained from option market prices and the Black-Scholes-Merton model with those expected theoretically if exchange rates follow the four stochastic processes specified above. The results of the comparison show that the pattern of implied volatilities is most consistent with the mixed Jump-Diffusion model.     

Intra–day Behavior of Treasury Sector Index Option Implied Volatilities around Macroeconomic Announcements

If option implied volatility is an unbiased, efficient forecast of future return volatility in the underlying asset, then we should be able to predict its path around macroeconomic announcements from responses in cash markets. Regressions show that volatilities rise the afternoon before announcements that move cash markets, and that post–announcement volatilities return to normal as rapidly as cash prices do. Although implied volatilities are predictable, the Treasury options market is efficient since informed traders do not earn arbitrage profits once we account for trading costs.     

The smirk in the S&P500 futures options prices: a linearized factor analysis

In the S&P500 futures options, we identify three factors, corresponding to movements in the underlying, parallel movements, and tilting of the cross section of implied volatilities (the “smirk factor”). We relate these factors non-linearly to movements in the option prices. They seem to be diffusive in nature, have significant associated risk premia, and can account for an overwhelming part of the option price movements. We interpret the options smirk, which is the notion that out-of-the-money (OTM) puts seem expensive relative to OTM calls, in terms of the prices of these risk factors. Going short OTM puts and long OTM calls, corresponding to the third factor, makes a profit on average, but this corresponds to its risk premium, and does not represent a market inefficiency. Our smirk factor is useful for hedging option portfolios, but seems unrelated to movements in the underlying, and does not fit into the framework of the jump-diffusion models.      

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.     

The Lead‐Lag Relationship Between Cash and Stock Index Futures in a New Market

This paper investigates the lead‐lag relationship in daily returns and volatilities between price movements of the FTSE/ATHEX‐20 and FTSE/ATHEX Mid‐40 stock index futures and the underlying cash indices in the relatively new futures market of Greece. Empirical results show that there is a bi‐directional relationship between cash and futures prices. However, futures lead the cash index returns, by responding more rapidly to economic events than stock prices. This speed is much higher in the more liquid FTSE/ATHEX‐20 market. Moreover, results indicate that futures volatilities spill information over to the corresponding cash market volatilities in both investigated futures markets, but volatilities in the cash markets have no effect on the volatilities of futures markets. Overall, it seems that new market information is disseminated faster in the futures market compared to the stock market. This implies that the futures markets can be used as price discovery vehicles, providing further evidence that derivatives markets contribute to completing and stabilising capital markets in Greece. A further finding of this study is that futures volume and disequilibrium effects between cash and futures prices are important variables in the explanation of volatilities in cash and futures markets.     

PRICING CURRENCY OPTIONS UNDER STOCHASTIC INTEREST RATES AND JUMP‐DIFFUSION PROCESSES

We investigate the effects of stochastic interest rates and jumps in the spot exchange rate on the pricing of currency futures, forwards, and futures options. The proposed model extends Bates's model by allowing both the domestic and foreign interest rates to move around randomly, in a generalized Vasicek term‐structure framework. Numerical examples show that the model prices of European currency futures options are similar to those given by Bates's and Black's models in the absence of jumps and when the volatilities of the domestic and foreign interest rates and futures price are negligible. Changes in these volatilities affect the futures options prices. Bates's and Black's models underprice the European currency futures options in both the presence and the absence of jumps. The mispricing increases with the volatilities of interest rates and futures prices. JEL classification: G13     

Volatility transmission in emerging European foreign exchange markets

This paper studies the dynamics of volatility transmission between Central European (CE) currencies and the EUR/USD foreign exchange using model-free estimates of daily exchange rate volatility based on intraday data. We formulate a flexible yet parsimonious parametric model in which the daily realized volatility of a given exchange rate depends both on its own lags as well as on the lagged realized volatilities of the other exchange rates. We find evidence of statistically significant intra-regional volatility spillovers among the CE foreign exchange markets. With the exception of the Czech and, prior to the recent turbulent economic events, Polish currencies, we find no significant spillovers running from the EUR/USD to the CE foreign exchange markets. To measure the overall magnitude and evolution of volatility transmission over time, we construct a dynamic version of the Diebold–Yilmaz volatility spillover index and show that volatility spillovers tend to increase in periods characterized by market uncertainty.     

Forecasting foreign exchange rates using idiosyncratic volatility

Average idiosyncratic stock volatility forecasts the bilateral exchange rates of the US dollar against major foreign currencies in and out of sample. The US dollar tends to appreciate after an increase in US idiosyncratic volatility. Similarly, ceteris paribus, German and Japanese idiosyncratic volatilities positively and significantly correlate with future US dollar prices of the Deutsche mark and the Japanese yen, respectively. Our results suggest that exchange rates are predictable.     

Crash-neutral currency carry trades

Currency carry trades exploiting violations of uncovered interest rate parity in G10 currencies deliver significant excess returns with annualized Sharpe ratios equal to or greater than those of equity market factors (1990–2012). Using data on out-of-the-money foreign exchange options, I compute returns to crash-hedged portfolios and demonstrate that the high returns to carry trades are not due to peso problems. A comparison of the returns to hedged and unhedged trades indicates crash risk premia account for at most one-third of the excess return to currency carry trades.     

Pricing errors and estimates of risk premia in factor models

In this paper, we consider the effect of the theoretical pricing error in the arbitrage pricing model on estimates of risk premia implied by the model. Under arbitrage pricing, the pricing error satisfies a strong bounding condition where for an infinite set of assets, the sum of squared pricing errors is bounded. We characterize the pricing error in terms of orders of probability and estimate an expected returns model which allows for pricing errors less than order one in probability. The principal finding of the paper is that misspecification of the pricing error and misspecification of the factor structure has no effect on the bias or mean squared error of the dominant risk premium. This implies that an exact form of arbitrage pricing can be used to estimate risk premia.     

A note on the no arbitrage condition for international financial markets

We consider an international financial market model that consists ofN currencies. The purpose is to derive a no arbitrage condition which is not affected by the choice of numéraire between theN currencies. As a result, we show that a finiteness condition for an arbitrary chosen currency and the no arbitrage condition for the basket currency are necessary and sufficient for the no arbitrage property of all theN currencies. Research supported in part by Nomura Foundation for Social Science and by the European Community Stimulation Plan for Economic Science contract Number SPES-CT91-0089. The authors thank an anonymous FEJM referee for helpful comments.     

State‐preference pricing and volatility indices

This study uses a state‐preference pricing approach to develop a state‐price volatility index (SVX), as a forecast for market future realised volatility. We show that SVX is a more efficient forecaster than CBOE VIX for 30‐day realised volatility of SPX returns, using both in‐the‐sample and out‐of‐the‐sample tests. This result is robust to different measures of realised market volatilities. We also show that SVX provides a better volatility forecast than other alternative measures, including the at‐the‐money implied volatilities and GARCH (1, 1) volatility. Our results provide a foundation for forecasting higher risk‐neutral moments using the same state prices.