In the aftermath of the financial crisis, institutions have been asked to reduce leverage in order to reduce risk. To address the effectiveness of this measure, we build a model of equity volatility that accounts for leverage. Our approach blends Merton’s insights on capital structure with traditional time-series models of volatility. We estimate that precautionary capital needs for the entire financial sector reached $2 trillion during the crisis. We also investigate the long-standing observation that equity volatility asymmetrically responds to positive and negative news. Volatility asymmetry is mostly explained by exposure to the aggregate market, not a mechanical leverage effect.

[Twenty-five years of volatility research has left the macroeconomic environment playing a minor role. This paper proposes modeling equity volatilities as a combination of macroeconomic effects and time series dynamics. High-frequency return volatility is specified to be the product of a slow-moving component, represented by an exponential spline, and a unit GARCH. This slow-moving component is the low-frequency volatility, which in this model coincides with the unconditional volatility. This component is estimated for nearly 50 countries over various sample periods of daily data. Low-frequency volatility is then modeled as a function of macroeconomic and financial variables in an unbalanced panel with a variety of dependence structures. It is found to vary over time and across countries. The low-frequency component of volatility is greater when the macroeconomic factors of GDP, inflation, and short-term interest rates are more volatile or when inflation is high and output growth is low. Volatility is higher not only for emerging markets and markets with small numbers of listed companies and market capitalization relative to GDP, but also for large economies. The model allows long horizon forecasts of volatility to depend on macroeconomic developments, and delivers estimates of the volatility to be anticipated in a newly opened market.]

I am pleased to offer a comment on this very interesting article by an author who is always in the forefront of the research on empirical financial models. This article presents data analysis that estabishes the stylized facts about stock market volatility around market crashes. He concludes that volatility is high during periods of stock market decline and that it gradually returns to more normal levels. In the case of 1987, the peak was higher than usual and the decline was more rapid. The article uses 28,000 daily observations but does not really estimate a usable model; instead, it explores the data by estimating highly overparameterized models that reveal important features of the data. I suggest that this be considered an exploratory investigation and that in the face of more parsimonious models, rather interesting and somewhat different conclusions are revealed. The basic model estimated by Schwert is a 22-order autoregression of daily returns with a heteroskedastic error standard deviation which is itself assumed to be a 22-order autoregression in the absolute errors. Even with 28,000 observations, there is apparently a lot of noise in the coefficients. To allow for a risk premium, the mean is related to the variance, and in this case it is therefore related to 22 lagged absolute residuals. This part of the model uses 66 parameters. An alternative model is a first-order generalized autoregressive conditionally heteroskedastic model with variance influencing the mean [GARCH (l, l)-m], with a first-order moving average to correct for non-synchronous trading as used in Engle, Lilien, and Robins (1987), French, Schwert, and Stambaugh (1987), or Chou (1988), following the earlier work of Engle (1982). This requires only four coefficients! In the context of the parsimonious model, the parameter regulating the risk-return trade-off can be interpreted as the median agent’s taste for risk or his coefficient of relative-risk aversion. One naturally asks whether this parameter is constant over time, and we then recognize that the Schwert parameterization cannot answer the question.

[We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model's flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state-price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.]

[This article investigates empirically how returns and volatilities of stock indices are correlated between the Tokyo and New York markets. Using intradaily data that define daytime and overnight returns for both markets, we find that Tokyo (New York) daytime returns are correlated with New York (Tokyo) overnight returns. We interpret this result as evidence that information revealed during the trading hours of one market has a global impact on the returns of the other market. In order to extract the global factor from the daytime returns of one market, we propose and estimate a signal-extraction model with GARCH processes.]

In the aftermath of the financial crisis, institutions have been asked to reduce leverage in order to reduce risk. To address the effectiveness of this measure, we build a model of equity volatility that accounts for leverage. Our approach blends Merton’s insights on capital structure with traditional time-series models of volatility. We estimate that precautionary capital needs for the entire financial sector reached $2 trillion during the crisis. We also investigate the long-standing observation that equity volatility asymmetrically responds to positive and negative news. Volatility asymmetry is mostly explained by exposure to the aggregate market, not a mechanical leverage effect. Received March 27, 2015; editorial decision February 25, 2017 by Editor Andrew Karolyi.

We introduce SRISK to measure the systemic risk contribution of a financial firm. SRISK measures the capital shortfall of a firm conditional on a severe market decline, and is a function of its size, leverage and risk. We use the measure to study top financial institutions in the recent financial crisis. SRISK delivers useful rankings of systemic institutions at various stages of the crisis and identifies Fannie Mae, Freddie Mac, Morgan Stanley, Bear Stearns, and Lehman Brothers as top contributors as early as 2005-Q1. Moreover, aggregate SRISK provides early warning signals of distress in indicators of real activity.

Twenty-five years of volatility research has left the macroeconomic environment playing a minor role. This paper proposes modeling equity volatilities as a combination of macro- economic effects and time series dynamics. High-frequency return volatility is specified to be the product of a slow-moving component, represented by an exponential spline, and a unit GARCH. This slow-moving component is the low-frequency volatility, which in this model coincides with the unconditional volatility. This component is estimated for nearly 50 countries over various sample periods of daily data. Low-frequency volatility is then modeled as a function of macroeconomic and financial variables in an unbalanced panel with a variety of dependence structures. It is found to vary over time and across countries. The low-frequency component of volatility is greater when the macroeconomic factors of GDP, inflation, and short-term interest rates are more volatile or when inflation is high and output growth is low. Volatility is higher not only for emerging markets and markets with small numbers of listed companies and market capitalization relative to GDP, but also for large economies. The model allows long horizon forecasts of volatility to depend on macroeconomic developments, and delivers estimates of the volatility to be anticipated in a newly opened market. The Author 2008. Published by Oxford University Press on behalf of the Society for Financial Studies. All rights reserved. For permissions, please e-mail: [email protected]., Oxford University Press.