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...

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...

Traditionally and understandably, the microscope of market microstructure has focused on attributes of single assets. Little theoretical attention and virtually no empirical work has been devoted to common determinants of liquidity nor to their empirical manifestation, correlated movements in...

We provide a model with overconfident risk neutral investors, and therefore no risk premia, in which a price-based portfolio such as HML earns positive expected returns and loads on fundamental macroeconomic variables. Furthermore, loadings on such portfolios are proxies for mispricing, and...

We explore the sharp uptrend in trading activity during recent years. Higher turnover has been associated with more frequent smaller trades, which have progressively formed a larger fraction of trading volume over time. Evidence indicates that secular decreases in trading costs have influenced...

The identical cash flow rights of Chinese A and B shares provide a natural experiment that allows us to explore how investor clienteles affect stock return patterns. Chinese domestic retail investors are responsible for the majority of trades in A shares, while foreign institutional investors...

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...