The scaling properties of historical volatility time series, which now appear to be universal, motivate the modeling of volatility as the exponential of fractional Brownian motion. This model can be understood as reflecting the high endogeneity of liquid markets and the long memory of order flow. The Rough Bergomi model which is the simplest corresponding model under Q fits the implied volatility surface remarkably well. As an application, we show how to forecast the variance swap curve. We also present a quasi-explicit expression for the characteristic function of a natural fractional generalization of the Heston model, a model which also fits the volatility surface very well, in contrast to the classical Heston model. Finally, we comment on the calibration of rough volatility models, which is still work in progress.
roughvolatilityminnesota2017_0.pdfroughvolatilityminnesota2017_0.pdfroughvolatilityminnesota2017_0.pdf
5:00 p.m. Tea, VinH 120
5:30 - 6:30 p.m., VinH 16
Presenters
Jim Gatheral
Jim Gatheral is researcher in the field of mathematical finance, who has contributed to the study of volatility as applied to the pricing and risk management of derivatives. A recurrent subject in his books and papers is the volatility smile, and he published in 2006 a book The Volatility Surface based on a course he taught for six years at New York University, along with Nassim Taleb. More recently his work has moved in the direction of market superstructure, especially as applied to algorithmic trading. He is the author of The Volatility Surface: A Practitioner's Guide. (2006, New Jersey: Wiley)
In March 2010, Jim Gatheral left his position at Merrill Lynch to assume a tenured full professor position at the Financial Engineering Masters Program at Baruch College where he is teaching volatility surface modeling and market microstructure. In April 2013, Jim was named Presidential Professor at Baruch College. Prior to this, he worked at Bank of America and Bankers Trust before heading the Equity Quantitative Analytics group at Merrill Lynch in 1996, where he was a managing director for 17 years. In 1998 he became a fellow of the Masters Program in Mathematical Finance at the Courant Institute of Mathematical Sciences at New York University, where he was an adjunct professor for 12 years.
Dr. Gatheral received his PhD in theoretical physics from Cambridge University (1983), and a B.Sc. in Mathematics and Natural Philosophy from the University of Glasgow.
