In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance...

This paper introduces a benchmark model for financial markets, which is based on the unique characterization of a benchmark portfolio that is chosen to be the growth optimal portfolio. The general structure of risk premia for asset prices and portfolios is derived. Furthermore, the short rate is...

Significant variation in the terms and volume of lending across classes of borrowers distinguished only by qualities independent of credit risk is often interpreted as evidence of inefficient or inequitable discrimination in credit markets. Increasing accuracy in the measure of credit risk...

We study a simple static economy with collateralized loan contracts and an incomplete asset market. We study whether economic forces operate to keep asset price equal to fundamentals in this economy. We find that asset prices may be higher than the valuation of any agent in the economy, i.e.,...

Return distributions in the class of pure jump limit laws are observed to reflect numerous asymmetries between the upward and downward motions of asset prices. The return distributions are modeled by self decomposable parametric laws with all parameters continuously responding to each other....

We study learning and uncertainty under the factor investing paradigm using an endogenous information model with correlated assets. As investors shift attention from firms towards systematic risk factors, stock prices become less informative, increasing systematic uncertainty and incentivizing...

There is a close link between prices of equity options and the default probability of a firm. We show that in the presence of positive expected equity recovery, standard methods that assume zero equity recovery at default misestimate the option-implied default probability. We introduce a simple...

The uncertainty around future changes to the Federal Reserve target rate varies over time. In our results, the main driver of uncertainty is a "path" factor signaling information about future policy actions, which is filtered from federal funds futures data. The uncertainty is highest when it...

In this paper, we present a novel method to extract the risk-neutral probability of default of a firm from American put option prices. Building on the idea of a default corridor proposed in Carr and Wu (2011), we derive a parsimonious closed-form formula for American put option prices from which...

This paper shows that changes in market participants' fear of rare events implied by crude oil options contribute to oil price volatility and oil return predictability. Using 25 years of historical data, we document economically large tail risk premia that vary substantially over time and...