Investors fear that surging volumes in short-term, especially same-day expiry (0DTE), options can destabilize markets by propagating large price jumps. Contrary to the intuition that 0DTE sellers predominantly generate delta-hedging flows that aggravate market moves, high open interest gamma in 0DTEs does not propagate past volatility. 0DTEs and underlying markets have become more integrated over time, leading to a marginally stronger link between the index volatility and 0DTE trading. Nonetheless, intraday 0DTE trading volume shocks do not amplify recent past index returns, inconsistent with the view that 0DTEs market growth intensifies market fragility.

About the speaker
Grigory Vilkov, Professor of Finance at the Frankfurt School of Finance and Management, holds an MBA from the University of Rochester and a Ph.D. from INSEAD, with further qualifications from Goethe University Frankfurt. He has been a professor at both Goethe University and the University of Mannheim.
His academic work focused on improving long-term portfolio strategies by building better expectations of risks, returns, and their dynamics. He is known for practical innovations in finance, such as developing forward-looking betas marketed by IvyDB OptionMetrics, establishing implied skewness and generalized lower bounds as cross-sectional stock characteristics, and creating measures for climate change exposure from earnings calls. His current research encompasses factor dispersions, factor and sector rotation, asset allocation with implied data, and machine learning in options analysis. 

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While the typical behaviors of stochastic systems are often deceptively oblivious to the tail distributions of the underlying uncertainties, the ways rare events arise are vastly different depending on whether the underlying tail distributions are light-tailed or heavy-tailed. Roughly speaking, in light-tailed settings, a system-wide rare event arises because everything goes wrong a little bit as if the entire system has conspired up to provoke the rare event (conspiracy principle), whereas, in heavy-tailed settings, a system-wide rare event arises because a small number of components fail catastrophically (catastrophe principle). In the first part of this talk, I will introduce the recent developments in the theory of large deviations for heavy-tailed stochastic processes at the sample path level and rigorously characterize the catastrophe principle for such processes. 
The empirical success of deep learning is often attributed to the mysterious ability of stochastic gradient descents (SGDs) to avoid sharp local minima in the loss landscape, as sharp minima are believed to lead to poor generalization. To unravel this mystery and potentially further enhance such capability of SGDs, it is imperative to go beyond the traditional local convergence analysis and obtain a comprehensive understanding of SGDs' global dynamics within complex non-convex loss landscapes. In the second part of this talk, I will characterize the global dynamics of SGDs building on the heavy-tailed large deviations and local stability framework developed in the first part. This leads to the heavy-tailed counterparts of the classical Freidlin-Wentzell and Eyring-Kramers theories. Moreover, we reveal a fascinating phenomenon in deep learning: by injecting and then truncating heavy-tailed noises during the training phase, SGD can almost completely avoid sharp minima and hence achieve better generalization performance for the test data.  

This talk is based on the joint work with Mihail Bazhba, Jose Blanchet, Bohan Chen, Sewoong Oh, Zhe Su, Xingyu Wang, and Bert Zwart.
 

One possible version of the Kirchberg—Phillips theorem states that simple, separable, nuclear, purely infinite C*-algebras are classified by KK-theory. In order to generalize this result to non-simple C*-algebras, Kirchberg first restricted his attention to those that absorb the Cuntz algebra O2 tensorially. C*-algebras in this class carry no KK-theoretical information in a strong sense, and they are classified by their ideal structure alone. It should be mentioned that, although this result is in Kirchberg’s work, its full proof was first published by Gabe. In joint work with Gábor Szabó, we showed a generalization of Kirchberg's O2-stable theorem that classifies G-C*-algebras up to cocycle conjugacy, where G is any second-countable, locally compact group. In our main result, we assume that actions are amenable, sufficiently outer, and absorb the trivial action on O2 up to cocycle conjugacy. In very recent work, I moreover show that the range of the classification invariant, consisting of a topological dynamical system over primitive ideals, is exhausted for any second-countable, locally compact group.

In this talk, I will recall the classification of O2-stable C*-algebras, and describe their classification invariant. Subsequently, I will give a short introduction to the C*-dynamical working framework and present the classification result for equivariant O2-stable actions. Time permitting, I will give an idea of how one can build a C*-dynamical system in the scope of our classification with a prescribed invariant.