As is well known, the classic Black­Scholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non­normal return innovations. Second,...

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular...

Levy processes can capture the behaviors of return innovations on a full range of financial securities. Applying stochastic time changes to the Levy processes randomizes the clock on which the processes run, thus generating stochastic volatilities and stochastic higher return moments. Therefore,...

In 1993, the Chicago Board of Options Exchange (CBOE) introduced the CBOE Volatility Index. This index has become the de facto benchmark for stock market volatility. On September 22, 2003, the CBOE revamped the definition and calculation of the volatility index, and back-calculated the new index...

This paper compares forecasts of real economic growth from models based on the stock market and bond market data. Although both contain information relevant for predicting GNP growth, the bond market delivers more accurate predictions. The bond market predictions are compared to the forecasts of...

One version of the consumption-based asset pricing model implies a linear relation between expected returns and expected consumption growth. This paper provides evidence that the expected real term structure contains information that can be used to forecast consumption growth. The evidence is...

We apply stochastic time change to Levy processes to generate a wide variety of tractable option pricing models. In particular, we prove a fundamental theorem that transforms the characteristic function of the time-changed Levy process into the Laplace transform of the stochastic time under...

We propose a method for optimal portfolio selection using a Bayesian decision theoretic framework that addresses two major shortcomings of the Markowitz approach: the ability to handle higher moments and estimation error. We employ the skew normal distribution which has many attractive features...

Final working paper version. "" Published version: The Review of Financial Studies, Volume 31, Issue 7, July 2018, pp. 2499–2552. Past fund performance does a poor job of predicting future outcomes. The reason is noise. Using a random effects framework, we reduce the noise by pooling...

Currently the real, inflation-adjusted, price of gold is almost as high as it was in January 1980 and August 2011. Since 1975, periods of high real gold prices have occurred during periods of elevated concern about high future price inflation. Five years after the real price peaks in January...