How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in...

Based on the typical positions of S&P 500 option market makers, we derive a funding illiquidity measure from quoted prices of S&P 500 derivatives. Our measure significantly affects the returns of leveraged managed portfolios; hedge funds with negative exposure to changes in funding illiquidity...

Asymmetric volatility concerns the relation of returns to future expected volatility. Much is known from option prices about the marginal risk-neutral distributions of S&P 500 returns and of relative changes in future expected volatility (VIX). While the bivariate risk-neutral distribution...