The equity trading landscape all over the world has changed dramatically in recent years. We have witnessed the advent of new trading venues and significant changes in the market shares of existing ones. We use an extensive panel dataset from the European equity markets to analyze the market...

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...

The equity trading landscape all over the world has changed dramatically in recent years. We have witnessed the advent of new trading venues and significant changes in the market shares of existing ones. We use an extensive panel dataset from the European equity markets to analyze the market...

The equity trading landscape all over the world has changed dramatically in recent years. We have witnessed the advent of new trading venues and significant changes in the market shares of existing ones. We use an extensive panel dataset from the European equity markets to analyze the market...

The equity trading landscape all over the world has changed dramatically in recent years. We have witnessed the advent of new trading venues and significant changes in the market shares of existing ones. We use an extensive panel dataset from the European equity markets to analyze the market...

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...

We study trading of Bitcoin against US dollar (BTCUSD) on exchanges in three continents, Bitfinex, Bitstamp and Coinbase Pro. We use a high frequency dataset that contains transactions and order book information. The BTCUSD market is highly liquid in terms of bid-ask spreads and order book...