In recent years, there has been substantive empirical evidence that stochastic volatility is rough. In other words, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter H0.5. In this paper,...

Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst parameter $H$. In this work, we provide a rigorous...

We develop a novel measure of volatility pass-through to assess international propagation of output volatility shocks to macroeconomic aggregates, equity prices, and currencies. An increase in country's output volatility is associated with a decrease in its output, consumption, and net exports....

Empirical evidence suggests that when the market becomes increasingly volatile, trading activities may be depressed or even halted. We develop a simple model to formally study the relationship between market volatility and asset liquidity in the real estate market. It is shown that an increase...

In the data, out-of-the-money (OTM) S&P 500 call and put options both have puzzling low average returns. Existing studies relate these results to models with non-standard preferences. We argue that the low returns on OTM index options are primarily due to the pricing of market volatility risk....