6:00 PM Seminar Begins

7:30 PM Reception

Hybrid Event:

Fordham University

McNally Amphitheater

140 West 62nd Street

New York, NY 10023

Free Registration!

For Virtual Attendees: Please select virtual instead of member type upon registration.

Abstract:

Option prices in the Black-Scholes model have a little-known determinant property: the determinants of out-of-the-money option prices with ordered strikes and maturities are positive. This property is called Total Positivity (TP) and implies additional constraints on option prices beyond those required by absence of arbitrage. Total positivity of order 2 (TP2) corresponds to 2 x 2 determinants and plays a special role. It holds for options with all strikes in the Black-Scholes model. It turns out to hold also for many (but not all) models beyond the Black-Scholes model, such as the Heston model, certain time-changed exponential Levy models and Gaussian mixture models. The talk presents the application of total positivity theory to option markets and discusses some of its implications. Empirical study on exchange-traded SP500 options shows that TP2 violations are infrequent, correct rapidly and can be used to construct profitable trading strategies.

Bio:

Dan Pirjol is an Associate Professor with the School of Business at Stevens Institute of Technology, where he teaches courses on financial engineering and risk management. Prior to joining Stevens he worked for more than 12 years in industry positions on Wall Street. His last position was with the model risk group at JP. Morgan, where he worked on models for counterparty credit risk and commodity derivatives. He received a PhD in theoretical physics from Mainz University, Germany.