Visioconférence en anglais le mercredi 2 février 2022
10h00-12h00 (Los Angeles) | 13h00-15h00 (New York) | 19h00-21h00 (Paris)CONFÉRENCE SLOAN : Régimes de prix
Organisée avec l'École polytechnique et l'Université de la Californie à Irvine
Ces dernières années, la modélisation non markovienne a été l’objet de beaucoup d'attention dans la modélisation financière. Il est fondamental et utile de comprendre comment un comportement non markovien ou fractionnaire, tel qu'observé à l'échelle macroscopique, peut résulter de modèles élaborés à l'échelle microscopique. Une telle analyse présente des similitudes, mais aussi des différences, avec l'analyse des systèmes physiques du point de vue des limites d'échelle. Cette conférence présente quelques aspects de l'analyse du comportement rugueux à l'échelle macro résultant de certaines dynamiques microscopiques.
VISIOCONFÉRENCE EN ANGLAIS
PROGRAMME
Quadratic Hawkes processes: A microfoundation for rough volatility models?
Jean-Philippe Bouchaud (Capital Fund Management/École polytechnique)
We discuss a natural generalization of the Hawkes processes that accounts for a feedback from past price trends and volatility onto current activity. The model naturally explains the power-law nature of price returns and the violation of time reversal invariance. It can be extended in various directions, in particular to model the activity in the order book and the occurrence of liquidity crises.
From no-arbitrage to rough volatility via market impact
Mathieu Rosenbaum (École polytechnique)
Slide presentation - Rosenbaum
Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that under no-arbitrage assumption, the market impact function can only be of a power-law type. Furthermore, we prove that this implies that the macroscopic price is diffusive with rough volatility, with a one-to-one correspondence between the exponent of the impact function and the Hurst parameter of the volatility. Hence, we simply explain the universal rough behavior of the volatility as a consequence of the no-arbitrage property. From a mathematical viewpoint, our study relies, in particular, on new results about hyper-rough stochastic Volterra equations.
Modeling rough covariance processes
Christa Cuchiero (University of Vienna)
The rough volatility paradigm asserts that the trajectories of assets’ volatility are rougher than Brownian motion, a revolutionary perspective that has changed certain persistent views of volatility. It provides via stochastic Volterra processes a universal approach to capture important features of time series and option price data, as well as microstructural foundations of markets. We provide an infinite dimensional point of view on stochastic Volterra processes, which makes it possible to dissolve a generic non-Markovanity of the at-first-sight naturally low dimensional volatility process. This approach makes it possible to go beyond the univariate case and to treat multivariate rough covariance models, in particular of affine and Wishart type, for more than one asset.
Discussion
Closing remarks
