The study of tail events has become a central preoccupation for academics, investors and policy makers, given the recent financial turmoil. However, the question on what differentiates a crash from a tail event remains unsolved.This article elaborates a new definition of stock market crash...

Asymmetric volatility in equity markets has been widely documented in finance, where two competing explanations, as considered in Bekaert and Wu (2000), are the financial leverage and the volatility feedback hypothesis. We explicitly test for the role of both hypotheses in explaining extreme...

We examine the impact of tail risk on the return dynamics of size, book-to-market ratio, momentum, and idiosyncratic volatility sorted portfolios. Our time-series analyses document significant portfolio return exposures to aggregate tail risk. In particular, portfolios that contain small, value,...

Following seminal works of Knight (1921) and Ellsberg (1961), we distinguish uncertainty from risk and examine the impact of aggregate uncertainty on return dynamics of size and book-to-market ratio sorted portfolios. Using VVIX as a proxy for aggregate uncertainty and controlling for market...

The seminal Modigliani-Miller (1958) theorem is a cornerstone of corporate finance theory. It provides conditions under which changes in a firm's capital structure do not affect its fundamental value. A recent controversial debate around the relevancy of the Modigliani-Miller theorem regarding...

Asymmetric volatility in equity markets has been widely documented in finance (Bekaert and Wu (2000)). We study asymmetric volatility for daily Samp;P 500 index returns and VIX index changes, thereby examining the relation between extreme changes in risk-neutral volatility expectations, i.e....

Dependence is an important issue in credit risk portfolio modeling and pricing. We discuss a straightforward common factor model of credit risk dependence, which is motivated by intensity models such as Duffie and Singleton (1998), among others. In the empirical analysis, we study dependence...

The market's assessment of the underlying asset's volatility as reflected in the option price is known as the implied volatility. Implied volatility indexes were created with the idea to provide an investor fear gauge since they represent a forecast of future average volatility. This article...

This paper is the first illustrated review of literature on local and implied volatility. It presents and discusses both concepts that are central in risk management. If local volatility is a relatively recent concept, implied volatility has emerged in the 70's as a global measure of uncertainty...

The relation between risk and return is very well documented in financial literature. While Sharpe (1964) proposed a linear relation between risk and return through the CAPM, Black (1976) pointed out later an asymmetric relation between these variables. Indeed, he noted that volatility was...