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...

Is there a short-term reversal effect outside the universe of individual stocks? To answer this, we investigate a comprehensive dataset of more than two centuries of returns on five major asset classes: equity indices, government bonds, treasury bills, commodities, and currencies. Contrary to...

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...

The ability to indicate factors which best explains common variation in stock returns, is crucial to construction of a correct pricing model and forecasting equity returns. Taking into account long finance literature, firm characteristics such as market capitalization, book-to-market ration, the...

Financialization of commodity markets has been a broadly discussed topic in recent years. However, its implications for commodity investors have not yet been fully explored. This paper concentrates on the macroeconomic determinants of commodity returns in financialized and non-financialized...

The financialization of commodity markets has recently become a broadly discussed phenomenon, but its implications for commodity investors to a large extent remain unknown. This article focuses on whether the potential benefits of passive investment strategies in the commodity futures markets...