Modeling the leverage effect with copulas and realized volatility

In this paper, we propose the use of static and dynamic copulas to study the leverage effect in the S&P 500 index. Copula models can conveniently separate the leverage effect from the marginal distributions of the return and its volatility. Daily volatility is proxied by a measure of realized volatility, which is constructed from high-frequency data. We uncover a significant leverage effect in the S&P 500 index, and this leverage effect is found to be changing over time in a highly persistent manner. Moreover the dynamic copula models are shown to outperform the static counterparts.     

Stochastic volatility and stochastic leverage

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new models. Furthermore, we give a detailed account on statistical properties of the new models.     

The leverage effect without leverage

We use experimental stock markets to add more evidence that Black's [1976. Proceedings of the 1976 Meeting of the Business and Economic Statistics Section. American Statistical Association, pp. 177–181] leverage effect in financial markets does not necessarily stem from the financial leverage of the firm. We surprisingly find a large number of markets in which the leverage effect is observed although the underlying asset does not exhibit any financial leverage at all.     

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.     

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...     

Option pricing under fast-varying and rough stochastic volatility

Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the origin. Another classic stylistic feature often assumed for the volatility is that it is mean reverting. In this paper it is shown that the price impact of a rapidly mean reverting rough volatility model coincides with that associated with fast mean reverting Markov stochastic volatility models. This reconciles the empirical observation of rough volatility paths with the good fit of the implied volatility surface to models of fast mean reverting Markov volatilities. Moreover, the result conforms with recent numerical results regarding rough stochastic volatility models. It extends the scope of models for which the asymptotic results of fast mean reverting Markov volatilities are valid. The paper concludes with a general discussion of fractional volatility asymptotics and their interrelation. The regimes discussed there include fast and slow volatility factors with strong or small volatility fluctuations and with the limits not commuting in general. The notion of a characteristic term structure exponent is introduced, this exponent governs the implied volatility term structure in the various asymptotic regimes.     

The effect of leverage on bargaining with a corporation

This paper shows that the choice of a capital structure by a firm affects the bargaining posture of its shareholders vis-a-vis its suppliers of specialized production factors. The pricing of the firm's securities and the choice of a capital structure are analyzed in light of this effect of debt financing.     

The January effect across volatility regimes

Using a Markov regime switching model, this article presents evidence of the well-known January effect on stock returns. The specification allows a distinction to be drawn between two regimes: one with high volatility and another with low volatility. We obtain a time-varying January effect that is, in general, positive and significant in both volatility regimes. However, this effect is larger in the high-volatility regime. In sharp contrast with most of the previous literature, we find two major results: (1) the January effect exists for all sizes of portfolio; (2) the negative correlation between the magnitude of the January effect and portfolio size fails across volatility regimes. Moreover, our evidence supports a slight decline in the January effect for all sizes of portfolio except the smallest, for which it is even larger.     

The effect of leverage on the cost of capital of US buyouts

This paper addresses the problem to assess the effect of leverage on the cost of capital for buyout performance analyses. It draws on a unique and proprietary set of data on 133 US buyouts between 1984 and 2004. For each of them, we determine a public market equivalent that matches it with respect to its timing and its systematic risk. We show that under realistic mimicking conditions, the average cost of capital is below the commonly used benchmark S&P 500. Thereby, we control for two important aspects: for the risks taken by lenders in the buyout transactions (which affects the sponsors’ risks), and for the corresponding cost of debt (which lowers the return of the public market equivalent). Only with borrowing and lending at the risk-free rate is the average cost of capital close to the average index return. This finding is particularly important as existing literature on that topic tends to rely on benchmarks without a proper risk-adjustment.     

Reassessing the effect of growth options on leverage

Results of empirical studies of the trade-off theory of capital structure indicate that an important, stable factor is missing from traditional leverage regression models. Our review of theory leads us to the hypothesis that the missing factor is related to profitable growth options (GOs). Specifically, the relationship between optimal leverage and the market-to-book assets ratio (MB), a measure of GOs, is negative and highly convex. In tests of static trade-off theory, we find that a convex (inverse exponential) transformation of MB substantially increases adjusted R² in leverage regressions, and partially subsumes the explanatory power of median industry leverage. Using the transformed MB variable also yields stronger results in tests of dynamic trade-off theory, including analyses of leverage evolution, speed of adjustment, and external financing activity.     

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 leverage effect puzzle: Disentangling sources of bias at high frequency

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation to be negative. To better understand the sources of the puzzle, we analyze the different asymptotic biases that are involved in high frequency estimation of the leverage effect, including biases due to discretization errors, to smoothing errors in estimating spot volatilities, to estimation error, and to market microstructure noise. This decomposition enables us to propose novel bias correction methods for estimating the leverage effect.     

The leverage of hedge funds

Long–short hedge funds are often very highly levered, despite the costs of leverage that became apparent during the LTCM crisis in 1998 and the more recent episode in 2008. This note explores potential market imperfections that may explain the use of leverage.     

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.     

Operating leverage,financial leverage,and equity risk

The analysis investigates the combined leverage effect of a fixed capacity decision (fixed cost) plus debt on the risk of equity returns. It is argued that the traditional DOL-DFL calculation is incorrect. A correct calculation is given, using the fact that the capacity decision is endogenous to the firm's decision process. The analysis reveals that the capacity decision partially offsets the effect on equity risk of increasing business risk or debt. However, this ability is lost at high levels of debt.     

The leverage effect puzzle: the case of European sovereign credit default swap market

One of the stylized facts about the behaviour of time series is that their volatility exhibits asymmetrical responses to good and bad news. In the case of stock markets, volatility seems to rise when the stock price decreases and fall when the stock price increases. This so-called “leverage effect” was first described by Black (Proceedings of the 1976 meeting of the business and economic statistics section, pp 177–181, 1976). The concept is not new and has already been comprehensively studied and implemented in many volatility models (GARCH and SV) in the form of an additional parameter in the volatility equation. However, there is no study or a theoretical explanation of the leverage effect in sovereign credit default swap spreads (hereinafter: sCDS). In this article, we discuss the possible behaviour of sCDS volatility and explain it by way of reference to the Prospect Theory by Kahneman and Tversky (Econometrica 47(2):263–292, 1979). We estimate a series of stochastic volatility models with the leverage effect, proposed by Yu (J Econom 127(2):165–178, 2005). In this model, the “leverage effect” is, in fact, the same as a coefficient of the correlation between the current return of an asset and its expected future volatility. We show that the effect does exist and differs across markets. As far as the safe European markets are concerned, the parameter is negative; in the case of extremely risky economies—it is positive. In markets of medium risk the effect varies depending on the relationship between the perceived risk and the value of the sCDS premium.     

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.     

Strategy as stretch and leverage

Global competition is not just product versus product or company versus company. It is mind-set versus mind-set. Driven to understand the dynamics of competition, we have learned a lot about what makes one company more successful than another. But to find the root of competitiveness--to understand why some companies create new forms of competitive advantage while others watch and follow--we must look at strategic mind-sets. For many managers, "being strategic" means pursuing opportunities that fit the company's resources. This approach is not wrong, Gary Hamel and C.K. Prahalad contend, but it obscures an approach in which "stretch" supplements fit and being strategic means creating a chasm between ambition and resources. Toyota, CNN, British Airways, Sony, and others all displaced competitors with stronger reputations and deeper pockets. Their secret? In each case, the winner had greater ambition than its well-endowed rivals. Winners also find less resource-intensive ways of achieving their ambitious goals. This is where leverage complements the strategic allocation of resources. Managers at competitive companies can get a bigger bang for their buck in five basic ways: by concentrating resources around strategic goals; by accumulating resources more efficiently; by complementing one kind of resource with another; by conserving resources whenever they can; and by recovering resources from the market-place as quickly as possible. As recent competitive battles have demonstrated, abundant resources can't guarantee continued industry leadership.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Employee representation and financial leverage

We analyze how direct employee voice affects financial leverage. German law mandates that firms’ supervisory boards consist of an equal number of employees’ and owners’ representatives. This requirement, however, applies only to firms with more than two thousand domestic employees. We exploit this discontinuity and the law’s introduction in 1976 for identification and find that direct employee power increases financial leverage. This is explained by a supply side effect: as banks’ interests are similar to those of employees, higher employee power reduces agency conflicts with debt providers, leading to better financing conditions. These findings reveal a novel mechanism of direct employee influence.