Time-changed Lévy processes and option pricing

The classic Black-Scholes option pricing model assumes that returns follow Brownian motion, but return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non-normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. Time-changed Lévy processes can simultaneously address these three issues. We show that our framework encompasses almost all of the models proposed in the option pricing literature, and it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.