Julien Guyon (NYU Tandon): Path-dependent Volatility скачать в хорошем качестве

Julien Guyon (NYU Tandon): Path-dependent Volatility

Note: The beginning of this video is cut off due to technical difficulties. Abstract: Recent empirical studies, extending the ARCH literature, have shown that the volatility of financial markets is mostly path-dependent, i.e. is very well explained by the history of past asset returns. After reviewing various arguments that all point to path-dependent volatility (PDV), we will present recent advances in PDV modeling. In particular, we will present new, simple, intuitive, low-dimensional Markovian PDV models which, unlike classical stochastic volatility models, use observable factors: a weighted average of past returns, and a weighted average of past returns squared. We will show that despite their simplicity, these models have a large predictive power and produce rich, intricate joint spot/volatility dynamics which capture many important stylized facts about volatility: strong endogeneity, a mix of short and long memory of realized variance and price trend, leverage effect, volatility clustering, roughness at the daily scale, Zumbach effect, jump-like behavior in absence of actual jumps, time-asymmetry of large volatility spikes, realistic implied volatility and implied volatility-of-volatility smiles. We will also show that these PDV models, which use a small number of parameters that all have a clear financial interpretation, can jointly fit S&P500 smiles, VIX smiles, and the historical asset price dynamics, thus reconciling historical and risk-neutral calibrations. Exogenous volatility shocks can be included to produce path-dependent stochastic volatility models. These new PDV models also raise interesting mathematical questions (wellposedness, nonnegativity, tractability) that will also be discussed. Speaker Bio: Julien Guyon is a professor of Applied Mathematics at École nationale des ponts et chaussées, one of the oldest and one of the most prestigious French Grandes Écoles, where he holds the BNP Paribas Chair Futures of Quantitative Finance, and a visiting associate professor in the Department of Finance and Risk Engineering at the NYU Tandon School of Engineering. He is also an adjunct professor in the Department of Mathematics at Columbia University (New York). Before joining Ecole des Ponts, Julien worked in the financial industry for 16 years, first in the Global Markets Quantitative Research team at Societe Generale in Paris (2006-2012), then as a senior quantitative analyst in the Quantitative Research group at Bloomberg L.P., New York (2012-2022). Julien was also previously an adjunct professor at the Courant Institute of Mathematical Sciences, NYU; at Baruch College, City University of New York; at Université Paris Diderot; and at École nationale des ponts et chaussées. Julien received the 2025 Quant of the Year award by Risk. He is also a Louis Bachelier Fellow. He serves as an Associate Editor of Finance & Stochastics, SIAM Journal on Financial Mathematics, Quantitative Finance, and Journal of Dynamics and Games. Julien co-authored the book Nonlinear Option Pricing (Chapman & Hall, 2014) with Pierre Henry-Labordere. He has published more than 25 articles in peer-reviewed journals (including Finance and Stochastics, SIAM Journal on Financial Mathematics, Quantitative Finance, Risk, Journal of Computational Finance, Annals of Applied Probability, Stochastic Processes and their Applications) and is a regular speaker at international conferences, both academic and professional. His main research interests include volatility and correlation modeling, option pricing, optimal transport, and numerical probabilistic methods. He is most famous for designing the particle method for smile calibration (with P.-H. Labordere), the Bergomi-Guyon expansion (an expansion of the smile in general stochastic volatility models at order 2 in small vol-of-vol), his works on path-dependent volatility (in particular devising the so-called Guyon-Lekeufack model), and his works on the joint calibration of S&P 500 and VIX smiles. A big soccer fan, Julien has also published articles on fairness in sports both in academic journals and in top-tier newspapers including The New York Times, The Times, Le Monde, and El País. Some of his suggestions for draws and tournament design have been adopted by FIFA and UEFA, including a new, fairer draw method for the FIFA World Cup (since 2018); a fairer format for the 2026 FIFA World Cup (adopted in March 2023); a new knockout bracket for the UEFA Euro (since 2020); and the draw method of the new UEFA Champions League league phase (since 2024). His paper "Risk of collusion: Will groups of 3 ruin the FIFA World Cup?" won the 2nd prize at the 2021 MIT Sloan Sports Analytics Conference, the biggest sports analytics event in the world.