Real-Time Volatility Estimation Under Zero Intelligence
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Date: 11-22-2006
Start Time:
6:00pm
End Time: 7:30pm
Speaker: Jim Gatheral, Merrill Lynch
Location: 412 Schapiro CEPSR, Davis Auditorium
Abstract
Accurate real-time volatility estimates are needed for many applications, including the real-time pricing of options. Also, high-frequency market data is widely available. The question then arises: given a time series of tick dates, how can realized volatility be estimated? The obvious estimator - the sum of squared returns between trades - is very biased by microstructure effects such as bid-ask bounce and so typically, practitioners are advised to drop most of the data and sample at most every five minutes or so. On the other hand, the points that are used, the greater the estimation error. The practical solution to this tradeoff between microstructure bias and estimation error has become a very active area of econometric research.
Various authors have suggested estimators and optimal sampling approaches based on a priori assumptions on the nature of the "microstructure noise" process. They often also confirm their results through Monte-Carlo simulation. However, it's not clear that then price process can be neatly decomposed into true price and noise processes and even if this were possible, it's not clear what the specification of the "microstructure noise" process should be.
We attempt to shed some light on this problem by simulating an artificial (zero-intelligence) market that has been shown to mimic some key properties of actual markets. Because our generating model also be constant, we know that the "true volatility" must also be constant and we can determine the "true volatility" through Monte Carlo simulation. It is then straightforward to take one realization of the price process and check to see how the various proposed estimators perform in estimating the "true volatility".
We conclude with firm practical recommendations on data sampling and efficient estimators.
Bio
Jim Gatheral is a managing director in Global Equities at Merrill Lynch and also an adjunct professor at the Courant Institute of Mathematical Sciences, New York University. He is the author of The Volatility Surface: A Practitioner's Guide, John Wiley & Sons, 2006. Since obtaining a PhD in theoretical physics from Cambridge University in 1983, Jim Gatheral has been involved in all of the major derivative product areas as bookrunner, risk manager, and quantitative analyst in London, Tokyo, and New York. From 1997 to 2005, he headed the Equity Quantitative Analytics group at Merrill Lynch. His current research focus is equity market microstructure and algorithmic trading.
Presentation