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.     

Central bank interventions and implied exchange rate correlations

This paper examines the effects of the foreign exchange market interventions by the Bank of Japan on the ex ante correlations between the JPY/USD, EUR/USD, and GBP/USD exchange rates. The correlation estimates used in the analysis are derived from the market prices of OTC currency options. The results show that central bank interventions significantly affect the market expectations about future exchange rate co-movements. In particular, we find that interventions tend to temporarily increase the ex ante correlations among the major exchange rates. However, our results also suggest that intervention episodes are associated with lower-than-average levels of exchange rate correlations.     

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.     

The implied volatility term structure of stock index options

This paper tests the expectations hypothesis of the term structure of implied volatility for several national stock market indexes. The tests indicate that the slope of at-the-money implied volatility over different maturities has predictive ability for future short-dated implied volatility, although not to the extent predicted by the expectations hypothesis. The low forecast power may be due to failure to control for a risk premium in the prices of the options. Evidence is presented that a time-varying risk premium proportional to the level of market volatility is consistent with the results.     

Probability weighting functions implied in options prices

The empirical pricing kernels estimated from index options are non-monotone (Rosenberg and Engle, 2002, Bakshi et al., 2010) and the corresponding risk-aversion functions can be negative (Aït-Sahalia and Lo, 2000, Jackwerth, 2000). We show theoretically that these and several other properties of empirical pricing kernels are consistent with rank-dependent utility model with probability weighting function, which overweights tail events. We also estimate the pricing kernels nonparametrically from the Standard & Poor's 500 index options and construct empirical probability weighting functions. The estimated probability weights typically have the inverse-S shape, which overweights tail events and is widely supported by the experimental decision theory.     

The effect of mergers on implied volatility of equity options

This paper uses a sample of 25 large mergers from 1996 to 2004 to study the effect of mergers on the implied volatilities of equity options. The results indicate a statistically significant increase in volatility beyond the amount predicted if the transaction were effectively nothing more than a portfolio combination of the target and acquirer. The disparity suggests that, at least for the first 18 months after the transaction becomes effective, market participants expect mergers to increase risk. Integration risk and uncertainty about the extent to which efficiency gains and greater market power are realized are possible explanations for the discrepancy.     

Modeling the evolution of implied CDO correlations

CDO tranche spreads (and prices of related portfolio-credit derivatives) depend on the market’s perception of the future loss distribution of the underlying credit portfolio. Applying Sklar’s seminal decomposition to the distribution of the vector of default times, the portfolio-loss distribution derived thereof is specified through individual default probabilities and the dependence among obligors’ default times. Moreover, the loss severity, specified via obligors’ recovery rates, is an additional determinant. Several (specifically univariate) credit derivatives are primarily driven by individual default probabilities, allowing investments in (or hedging against) default risk. However, there is no derivative that allows separately trading (or hedging) default correlations; all products exposed to correlation risk are contemporaneously also exposed to default risk. Moreover, the abstract notion of dependence among the names in a credit portfolio is not directly observable from traded assets. Inverting the classical Vasicek/Gauss copula model for the correlation parameter allows constructing time series of implied (compound and base) correlations. Based on such time series, it is possible to identify observable variables that describe implied correlations in terms of a regression model. This provides an economic model of the time evolution of the market’s view of the dependence structure. Different regression models are developed and investigated for the European CDO market. Applications and extensions to other markets are discussed.     

Tests of the foreign exchange risk premium using the expected second moments implied by option pricing

This paper utilizes the second moment expectations implied by currency option pricing to demonstrate that these expectations are systematically related to expected return differentials across assets denominated in different currencies. Because the measured deviations from uncovered interest rate parity are tied to variables which theory links to the risk premium, the results provide substantial evidence that a risk premium does indeed exist, as opposed to the alternative of a violation of rational expectations. However, like previous attempts, the data do not support an explicit mean-variance formulation of the risk premium.     

On the seasonality in the implied volatility of electricity options

Seasonality is an important topic in electricity markets, as both supply and demand are dependent on the time of the year. Clearly, the level of prices shows a seasonal behaviour, but not only this. Also, the price fluctuations are typically seasonal. In this paper, we study empirically the implied volatility of options on electricity futures, investigate whether seasonality is present and we aim at quantifying its structure. Although typically futures prices can be well described through multi-factor models including exponentially decreasing components, we do not find evidence of exponential behaviour in our data set. Generally, a simple linear shape reflects the squared volatilities very well as a curve depending on the time to maturity. Moreover, we find that the level of volatility exhibits clear seasonal patterns that depend on the delivery month of the futures. Furthermore, in an out-of-sample analysis we compare the performance of several implementations of seasonality in the one-factor framework.     

Predictable dynamics in implied volatility surfaces from OTC currency options

Recent empirical studies report predictable dynamics in the volatility surfaces that are implied by observed index option prices, such as those prescribed by general equilibrium models. Using an extensive data set from the over-the-counter options market, we document similar predictability in the factors that capture the daily variation of surfaces implied by options on 25 different foreign exchange rates. We proceed to demonstrate that simple vector autoregressive specifications for the factors can help produce accurate out-of-sample forecasts of the systematic component of the surface at short horizons. Profitable delta-hedged positions can be set up based on these forecasts; however, profits disappear when typical transaction costs are taken into account and when trading rules on wide segments of the surface are sought.     

Evaluating cross-sectional forecasting models for implied cost of capital

The computation of implied cost of capital (ICC) is constrained by the lack of analyst forecasts for half of all firms. Hou et al. (J Account Econ 53:504–526, 2012, HVZ) present a cross-sectional model to generate forecasts in order to compute ICC. However, the forecasts from the HVZ model perform worse than those from a naïve random walk model and the ICCs show anomalous correlations with risk factors. We present two parsimonious alternatives to the HVZ model: the EP model based on persistence in earnings and the RI model based on the residual income model from Feltham and Ohlson (Contemp Account Res 11:689–732, 1996). Both models outperform the HVZ model in terms of forecast bias, accuracy, earnings response coefficients, and correlations of the ICCs with future returns and risk factors. We recommend that future research use the RI model or the EP model to generate earnings forecasts.     

The crisis in the foreign exchange market

We provide an overview of the important events of the recent global financial crisis and their implications for exchange rates and market dynamics. Our goal is to catalogue all that was truly of major importance in this episode. We also construct a quantitative measure of crises that allows for a comparison of the current crisis to earlier events. In addition, we address whether one could have predicted costly events before they happened in a manner that would have allowed market participants to moderate their risk exposures and yield better returns from currency speculation.     

Market pricing of executive stock options and implied risk preferences

When managers get to trade in options received as compensation, their trading prices reveal several aspects of subjective option pricing and risk preferences. Two subjective pricing models are fitted to show that executive stock option prices incorporate a subjective discount. It depends positively on implied volatility and negatively on option moneyness. Further, risk preferences are estimated using the semiparametric model of Aït-Sahalia and Lo (2000). The results suggest that relative risk aversion is just above 1 for a certain stock price range. This level of risk aversion is low but reasonable, and it may be explained by the typical manager being wealthy and having low marginal utility. Related to risk aversion, it is found that marginal rate of substitution increases considerably in states with low stock prices.     

Forecasting foreign exchange volatility: Why is implied volatility biased and inefficient? And does it matter?

Research has consistently found that implied volatility is a conditionally biased predictor of realized volatility across asset markets. This paper evaluates explanations for this bias in the market for options on foreign exchange futures. Several recently proposed solutions – including a model of priced volatility risk – fail to explain a significant portion of the conditional bias found in implied volatility. Further, while implied volatility fails to subsume econometric forecasts in encompassing regressions, these forecasts do not significantly improve delta-hedging performance. Thus this paper argues that statistical metrics are inappropriate measures of the information content of implied volatility. Implied volatility appears much more useful when measured by a more relevant, economic metric.     

The predictive power of the implied volatility of options traded OTC and on exchanges

This paper investigates the efficiency of stock index options traded over-the-counter (OTC) and on the exchanges in Hong Kong and Japan. Our findings suggest that implied volatility is superior to either historical volatility or a GARCH-type volatility forecast in predicting future volatility in both the OTC and exchange markets. This paper is also one of the first to compare the predictive power of the implied volatility of stock index options traded OTC to that of exchange-traded stock index options. Our evidence suggests that the OTC market is more efficient than the exchanges in Japan, but that the opposite is true in Hong Kong.     

Central bank intervention and the volatility of foreign exchange rates: evidence from the options market

This paper tests the effects of central bank intervention on the ex ante volatility of $/DM and $/yen exchange rates between 1985 and 1991. In contrast to previous research which employed GARCH estimates of conditional volatility, we estimate ex ante volatility using the implied volatilities of currency option prices. We also control for the effects of other macroeconomic announcements. We find little support for the hypothesis that central bank intervention decreases expected exchange rate volatility. Instead, central bank intervention is generally associated with a positive change in ex ante exchange rate volatility, or with no change.     

Pricing of foreign exchange options under the MPT stochastic volatility model and the CIR interest rates

We consider an extension of the model proposed by Moretto, Pasquali, and Trivellato [2010. “Derivative Evaluation Using Recombining Trees under Stochastic Volatility.” Advances and Applications in Statistical Sciences 1 (2): 453–480] (referred to as the MPT model) for pricing foreign exchange (FX) options to the case of stochastic domestic and foreign interest rates driven by the Cox, Ingersoll, and Ross dynamics introduced in Cox, Ingersoll, and Ross [1985. “A Theory of Term Structure of Interest Rates.” Econometrica 53(2): 385–408]. The advantage of the MPT model is that it retains some crucial features of Heston's stochastic volatility model but, as demonstrated in Moretto, Pasquali, and Trivellato [2010. “Derivative Evaluation Using Recombining Trees under Stochastic Volatility.” Advances and Applications in Statistical Sciences 1 (2): 453–480], it is better suited for discretization through recombining lattices, and thus it can also be used to value and hedge exotic FX products. In the model examined in this paper, the instantaneous volatility is correlated with the exchange rate dynamics, but the domestic and foreign short-term rates are assumed to be mutually independent and independent of the dynamics of the exchange rate. The main result furnishes a semi-analytical formula for the price of the FX European call option, which hinges on explicit expressions for conditional characteristic functions.     

Sovereign rating actions and the implied volatility of stock index options

This paper examines the interaction between the equity index option market and sovereign credit ratings. S&P and Moody's signals exhibit strong impact on option-implied volatility while Fitch's influence is less significant. Moody's downgrades reduce the market uncertainty over the rated countries' equity markets. Strong causal relationships are found between movements in the option-implied volatility and all credit signals released by S&P and Fitch, but only actual rating changes by Moody's, implying differences in rating agencies' policies. The presence of additional ratings tends to reduce market uncertainty. The findings highlight the importance of rating information in the price discovery process and offer policy implications.     

The time-varying diversifiability of corporate foreign exchange exposure

Estimating comovement measures for a large set of bilateral foreign exchange (FX) rates, I explore the relation between firm-level FX exposure and its time-varying diversifiability. For a sample of U.S. firms, the magnitude of FX exposure appears to increase during periods of low currency risk diversifiability. Additional results suggest that the introduction of the euro exacerbated the effect of diversifiability on developed market currency exposure. Moreover, the low diversifiability of emerging market currencies seems to have a stronger effect on FX exposure than the low diversifiability of developed market currencies.