Using Nasdaq ITCH data, we argue that the standard self-financing condition of the Black-Scholes theory needs to be modified to account for trading behavior in the high-frequency markets. A consequence of this empirical study was the realization that the time evolutions of traders’ inventories should not be modeled by differentiable functions of time — as in most theoretical models — but with unbounded variations functions instead. We use econometric statistical tests to confirm the presence of a Brownian motion term in the inventories of traders on the Toronto Stock Exchange. Finally, we extend the theoretical analysis of a known optimal execution model to include this Brownian component, and we compare the actual behaviors to some day traders to the “optimal” behavior suggested by the model.
Presenter: René Carmona
Dr. René Carmona is an associate member of Princeton University's Department of Mathematics, a member of the Program in Applied and Computational Mathematics, and Director of Graduate Studies of the Bendheim Center for Finance, where he oversees the Master in Finance program. He obtained a Ph.D. in probability from Marseille University, where he held his first academic job. Prof. Carmona is a Fellow of the Institute of Mathematical Statistics, of the Society for Industrial and Applied Mathematics, and of the American Mathematical Society. He is the founding chair of the SIAM Activity Group on Financial Mathematics and Engineering, a founding editor of the Electronic Journal of Probability and Electronic Communications in Probability, and the SIAM Journal on Financial Mathematics. His publications include more than 100 articles and 11 books in probability, statistics, mathematical physics, signal analysis and financial mathematics.
About this series
The Financial Engineering Seminar Series is a recurring event featuring thought leaders from industry and academia, who bring their experiences to a variety of important topics in this discipline.