The threshold effect in expected volatility: a model based on asymmetric information

This article develops theoretical insight into the thresholdeffect in expected volatility, which means that large shocksare less persistent in volatility than small shocks. The modeluses the Kyle-Admati-Pfleiderer setup with liquidity traders,informed traders, and a market maker. Information is modeledas a GARCH process. It is shown that the GARCH process for informationis transformed into a TARCH process (for 'threshold GARCH')for the market price changes. Working with information flowsallows one to derive implications for trading volume and marketliquidity which provide the basis for a more complete test ofthe model.     

On expectations,term premiums and the volatility of long-term interest rates

Shiller has shown that the variance of the holding-period yield on long-term bonds may frequently exceed a bound implied by the rational expectations model of the term structure. This paper extends Shiller's variance inequality to allow for the possible presence of time-varying term premiums. The paper then explores the question of whether term premiums, or perhaps transactions costs, are likely to reverse prior findings of excess volatility.     

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.     

Domestic and foreign disturbances in an optimizing model of exchange-rate determination

This paper analyzes the effects of various disturbances of domestic and foreign origin in a small open economy under imperfect capital mobility in which the behavioral relationships are divided from optimization by the private sector. In this model the domestic economy jumps instantaneously to its new equilibrium following a change in either the domestic monetary growth rate or domestic fiscal policy. In response to a disturbance in either the foreign interest rate or inflation rate, the economy undergoes an initial partial jump towards its new equilibrium, which it thereafter approaches gradually. The implications of these results for exchange-rate adjustments and the insulation properties of flexible exchange rates are discussed.     

The information content of implied volatilities and model-free volatility expectations: Evidence from options written on individual stocks

We measure the volatility information content of stock options for individual firms using option prices for 149 US firms and the S&P 100 index. We use ARCH and regression models to compare volatility forecasts defined by historical stock returns, at-the-money implied volatilities and model-free volatility expectations for every firm. For 1-day-ahead estimation, a historical ARCH model outperforms both of the volatility estimates extracted from option prices for 36% of the firms, but the option forecasts are nearly always more informative for those firms that have the more actively traded options. When the prediction horizon extends until the expiry date of the options, the option forecasts are more informative than the historical volatility for 85% of the firms. However, at-the-money implied volatilities generally outperform the model-free volatility expectations.     

Non-homogeneous volatility correlations in the bivariate multifractal model

In this paper, we consider an extension of the recently proposed bivariate Markov-switching multifractal model of Calvet, Fisher, and Thompson [2006. “Volatility Comovement: A Multifrequency Approach.” Journal of Econometrics 131: 179–215]. In particular, we allow correlations between volatility components to be non-homogeneous with two different parameters governing the volatility correlations at high and low frequencies. Specification tests confirm the added explanatory value of this specification. In order to explore its practical performance, we apply the model for computing value-at-risk statistics for different classes of financial assets and compare the results with the baseline, homogeneous bivariate multifractal model and the bivariate DCC-GARCH of Engle [2002. “Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models.” Journal of Business & Economic Statistics 20 (3): 339–350]. As it turns out, the multifractal model with heterogeneous volatility correlations provides more reliable results than both the homogeneous benchmark and the DCC-GARCH model.     

The microstructural foundations of leverage effect and rough volatility

We show that typical behaviors of market participants at the high frequency scale generate leverage effect and rough volatility. To do so, we build a simple microscopic model for the price of an asset based on Hawkes processes. We encode in this model some of the main features of market microstructure in the context of high frequency trading: high degree of endogeneity of market, no-arbitrage property, buying/selling asymmetry and presence of metaorders. We prove that when the first three of these stylized facts are considered within the framework of our microscopic model, it behaves in the long run as a Heston stochastic volatility model, where a leverage effect is generated. Adding the last property enables us to obtain a rough Heston model in the limit, exhibiting both leverage effect and rough volatility. Hence we show that at least part of the foundations of leverage effect and rough volatility can be found in the microstructure of the asset.     

Seasonality in stock returns and volatility: The Ramadan effect

Calendar anomalies in stock returns are well documented. Less obvious is the existence of seasonality in return volatility associated with moving calendar events such as the Muslim holy month of Ramadan. Using a GARCH specification and data for the Saudi Arabian stock market – now the largest stock market in the Muslim world – this paper documents a systematic pattern of decline in volatility during Ramadan, implying a predictable variation in the market price of risk. An examination of trading data shows that this anomaly appears to be consistent with a decline in trading activity during Ramadan. Evidence of systematic decline in volatility during Ramadan has significant implications for pricing of securities especially option-like products and asset allocation decisions by investors in the Islamic countries.     

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.     

Gamma expansion of the Heston stochastic volatility model

We derive an explicit representation of the transitions of the Heston stochastic volatility model and use it for fast and accurate simulation of the model. Of particular interest is the integral of the variance process over an interval, conditional on the level of the variance at the endpoints. We give an explicit representation of this quantity in terms of infinite sums and mixtures of gamma random variables. The increments of the variance process are themselves mixtures of gamma random variables. The representation of the integrated conditional variance applies the Pitman–Yor decomposition of Bessel bridges. We combine this representation with the Broadie–Kaya exact simulation method and use it to circumvent the most time-consuming step in that method.     

The volatility target effect in structured investment products with capital protection

Designing a structured investment product with capital protection which would be characterized by high capital protection level as well as high equity participation rate is a challenging task in the current market environment. Low interest rates and high volatility levels negatively affect the above key parameters of such investment products. One way to increase the participation rate of a structured investment product with a fixed capital protection level is to use a volatility target (VolTarget) strategy as an underlying asset for a financial option embedded in such a product. We introduce an extended VolTarget mechanism with interest rate dependent volatility target levels and provide a detailed comparative numerical study of European options linked to VolTarget strategies within a hybrid Heston–Vasi?ec model with stochastic volatility and stochastic interest rate.     

The effect of Regulation Fair Disclosure on expectations management: International evidence

We examine whether Regulation Fair Disclosure (Reg FD) was effective in limiting the expectations management of US firms as well as ADR and foreign-listed firms to meet or beat analysts’ earnings forecasts. Domestic US firms are required to comply with Reg FD; however, ADR firms are explicitly exempted from its provisions. Thus, ADR firms are thought to represent a control against which US firm expectations management is measured. We find a decrease in expectations management for both US and ADR firms. We find that the post-Reg-FD changes for US and ADR firms are not significantly different. This suggests Reg FD was not effective in limiting forecast guidance or, alternatively, both US and ADR firms responded to Reg FD by reducing forecast guidance. We provide additional evidence that ADR firms experienced a significant decrease in expectations management relative to other foreign-listed firms suggesting that ADR firms voluntarily complied with Reg FD. Overall, our evidence suggests that Reg FD worked to reduce expectations management to meet or beat expectations for both US and ADR firms.     

Rational expectations and the expectations model of the term structure: A test using weekly data

This paper tests the joint hypothesis of rational expectations model of the term structure for three- and six-month Treasury bills. Previous studies are extended in two main directions. First, the joint hypothesis is tested using weekly data for Treasury bills maturing in exactly 13 and 26 weeks beginning in 1970 and ending in 1979. In contrast, previous studies using comparable data have typically discarded 12/13 of the sample to a form a nonoverlapping data set. Second, a more complete set of possible determinants of time-varying premiums is tested.     

Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model

We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to returns, we consider a filtered FIEGARCH-in-mean (FIEGARCH-M) effect in the return equation. The filtering of the volatility-in-mean component thus allows the co-existence of long memory in volatility and short memory in returns. We present an application to the daily CRSP value-weighted cum-dividend stock index return series from 1926 through 2006 which documents the empirical relevance of our model. The volatility-in-mean effect is significant, and the FIEGARCH-M model outperforms the original FIEGARCH model and alternative GARCH-type specifications according to standard criteria.     

The impact of the leverage effect on the implied volatility smile: evidence for the German option market

Review of Derivatives Research - It is a widely known theoretical derivation, that the firm’s leverage is negatively related to volatility of stock returns, although the empirical evidence is...     

Detecting volatility persistence in GARCH models in the presence of the leverage effect

Most asset prices are subject to significant volatility. The arrival of new information is viewed as the main source of volatility. As new information is continually released, financial asset prices exhibit volatility persistence, which affects financial risk analysis and risk management strategies. This paper proposes a nonlinear regime-switching threshold generalized autoregressive conditional heteroskedasticity model which can be used to analyse financial data. The empirical results based on quasi-maximum likelihood estimation presented in this paper suggest that the proposed model is capable of extracting information about the sources of volatility persistence in the presence of the leverage effect.     

On the qualitative effect of volatility and duration on prices of Asian options

We show that under the Black–Scholes assumption the price of an arithmetic average Asian call option with fixed strike increases with the level of volatility. This statement is not trivial to prove and for other models in general wrong. In fact we demonstrate that in a simple binomial model no such relationship holds. Under the Black–Scholes assumption however, we give a proof based on the maximum principle for parabolic partial differential equations. Furthermore we show that an increase in the length of duration over which the average is sampled also increases the price of an arithmetic average Asian call option, if the discounting effect is taken out. To show this, we use the result on volatility and the fact that a reparametrization in time corresponds to a change in volatility in the Black–Scholes model. Both results are extremely important for the risk management and risk assessment of portfolios that include Asian options.     

The effect of derivative assets on information acquisition and price behavior in a rational expectations equilibrium

This article shows that introducing derivative assets increasesincentives to collect information about asset payoffs. The increasein information collection makes the price of the underlyingasset more informative and causes the expected price to increase.Extending the model to a dynamic setting with multiple riskyassets, we find the introducing derivative assets for one assetincreases the expected prices of positively correlated assetsand reduces price reaction to future earnings announcements.These findings are consistent with the bulk of the empiricalevidence on the relationship between the introduction of derivativeassets and the behavior of asset prices.