Financial Seminar Series: A Simple Probabilistic Representation of an Arbitrage-free Implied Variance Rate | Hanlon Financial Systems Center

Financial Seminar Series: A Simple Probabilistic Representation of an Arbitrage-free Implied Variance Rate

Financial Seminar Series: A Simple Probabilistic Representation of an Arbitrage-free Implied Variance Rate

Event Location: 
Babbio Center 104
Event Time: 
Thursday, November 30, 2017 - 5:00pm to 6:00pm

Dr. Peter Carr

The Chair of the Finance and Risk Engineering Department at NYU Tandon School of Engineering

ABSTRACT

When the variance rates implied from option prices differ across strike prices, at most one of them can be interpreted as the variance rate of the underlying security price. We develop an arbitrage-free option pricing model with four stochastic state variables, one of which is the underlying security price. We show how to successively explicitly determine the other three state variables from three given co-terminal arbitrage-free implied variance rates. The resulting calibrated implied variance rate smile is given a simple probabilistic representation. To our knowledge, this is the first non-flat implied variance rate smile enjoying any probabilistic interpretation.

BIOGRAPHY

Dr. Peter Carr is the Chair of the Finance and Risk Engineering Department at NYU Tandon School of Engineering. He has headed various quant groups in the financial industry for the last twenty years. He also presently serves as a trustee for the National Museum of Mathematics and WorldQuant University. Prior to joining the financial industry, Dr. Carr was a finance professor for 8 years at Cornell University, after obtaining his Ph.D. from UCLA in 1989. He has over 85 publications in academic and industry-oriented journals and serves as an associate editor for 8 journals related to mathematical finance. He was selected as Quant of the Year by Risk Magazine in 2003 and Financial Engineer of the Year by IAQF/Sungard in 2010. From 2011 to 2014, Dr. Carr was included in Institutional Investor's Tech 50, an annual listing of the 50 most influential people in financial technology.