Motivated by the implications from a stylized self-contained general equilibrium model
incorporating the effects of time-varying economic uncertainty, we show that the difference …

We examine the relationship between volatility and past and future returns using high-
frequency aggregate equity index data. Consistent with a prolonged “leverage” effect, we …

There is ongoing debate about the apparent weak or negative relation between risk
(conditional variance) and expected returns in the aggregate stock market. We develop and …

We first propose a reduced-form model in discrete time for S&P 500 volatility showing that
the forecasting performance can be significantly improved by introducing a persistent …

This paper provides a simple theoretical framework for assessing the empirical linkages
between returns and realized and implied volatilities. First, we show that whereas the …

A complete guide to the theory and practice of volatility models in financial engineering
Volatility has become a hot topic in this era of instant communications, spawning a great …

Prior studies find that the CBOE volatility index (VIX) predicts returns on stock market
indices, suggesting implied volatilities measured by VIX are a risk factor affecting security …

This paper explores the time-series relation between expected returns and risk for a large
cross section of industry and size/book-to-market portfolios. I use a bivariate generalized …

This paper is motivated by Bitcoin's rapid ascension into mainstream finance and recent
evidence of a strong relationship between Bitcoin and US stock markets. It is also motivated …

Univariate dependencies in market volatility, both objective and risk neutral, are best
described by long-memory fractionally integrated processes. Meanwhile, the ex post …