Peter Carr Seminar Series: Petter Kolm and Sebastien Bossu

4 pm | Petter Kolm

Title

Identifying Patterns in Financial Markets: Extending the Statistical Jump Model for Regime Identification

Abstract

Regime-driven models are popular for addressing temporal patterns in both financial market performance and underlying stylized factors, wherein a regime describes periods with relatively homogeneous behavior. Recently, statistical jump models have been proposed to learn regimes with high persistence, based on clustering temporal features while explicitly penalizing jumps across regimes. In this article, we extend the jump model by generalizing the discrete hidden state variable into a probability vector over all regimes. This allows us to estimate the probability of being in each regime, providing valuable information for downstream tasks such as regime-aware portfolio models and risk management. Our model’s smooth transition from one regime to another enhances robustness over the original discrete model. We provide a probabilistic interpretation of our continuous model and demonstrate its advantages through simulations and real-world data experiments. The interpretation motivates a novel penalty term, called mode loss, which pushes the probability estimates to the vertices of the probability simplex thereby improving the model’s ability to identify regimes. We demonstrate through a series of empirical and real world tests that the approach outperforms traditional regime-switching models. This outperformance is pronounced when the regimes are imbalanced and historical data is limited, both common in financial markets.

Bio

Petter Kolm was awarded “Quant of the Year” in 2021 by Portfolio Management Research (PMR) and Journal of Portfolio Management (JPM) for his contributions to the field of quantitative portfolio theory. Petter is a frequent speaker, panelist, and moderator at academic and industry conferences and events. He is a member of the editorial boards of the International Journal of Portfolio Analysis and Management (IJPAM), Journal of Financial Data Science (JFDS), Journal of Investment Strategies (JoIS), and Journal of Portfolio Management (JPM). Petter is an Advisory Board Member of Aisot, Axyon, GoQuant, and Volatility and Risk Institute at NYU Stern. He is also on the Board of Directors of the International Association for Quantitative Finance (IAQF) and Society of Quantitative Analysts (SQA), and Scientific Advisory Board Member of the Artificial Intelligence Finance Institute (AIFI).

Petter is the co-author of several well-known finance books including, Financial Modeling of the Equity Market: From CAPM to Cointegration (Wiley, 2006); Trends in Quantitative Finance (CFA Research Institute, 2006); Robust Portfolio Management and Optimization (Wiley, 2007); and Quantitative Equity Investing: Techniques and Strategies (Wiley, 2010). Financial Modeling of the Equity Markets was among the “Top 10 Technical Books” selected by Financial Engineering News in 2006.

As a consultant and expert witness, Petter provides services in areas including alternative data, data science, econometrics, forecasting models, high frequency trading, machine learning, portfolio optimization with transaction costs, quantitative and systematic trading, risk management, robo-advisory, smart beta strategies, trading strategies, transaction costs, and tax-aware investing.

He holds a Ph.D. in Mathematics from Yale University; an M.Phil. in Applied Mathematics from the Royal Institute of Technology, Stockholm, Sweden; and an M.S. in Mathematics from ETH Zurich, Switzerland.

5 pm | Sebastien Bossu

Title

Spanning Multi-Asset Payoffs with ReLUs

Abstract

We propose a distributional formulation of the spanning problem of a multi-asset payoff by vanilla basket options. This problem is shown to have a unique solution if and only if the payoff function is even and absolutely homogeneous, and we establish a Fourier-based formula to calculate the solution. Financial payoffs are typically piecewise linear, resulting in a solution that may be derived explicitly, yet may also be hard to exploit numerically. One-hidden-layer feedforward neural networks instead provide a natural and efficient numerical alternative for discrete spanning. We test this approach for a selection of archetypal payoffs and obtain better hedging results with vanilla basket options compared to industry-favored approaches based on single-asset vanilla hedges. Reference paper: https://arxiv.org/abs/2403.14231 (joint work with Stéphane Crépey and Hoang-Dung Nguyen, Université Paris-Cité).

Bio

After 20 years of industry experience, Sébastien Bossu was appointed Assistant Professor of Mathematics and Statistics at UNC Charlotte. He has been principal at his startup investment and consulting company in New York City since 2011, and also served as part-time faculty at various institutions including NYU Courant and Johns Hopkins Carey Business School. Prior to moving to the U.S., Sébastien was a Director and Head of the Equity Derivatives Structuring team at Dresdner Kleinwort (now Commerzbank) in London, an Associate at J.P. Morgan in London, and Jr. Trader at Goldman Sachs in Paris. He has written two textbooks on equity derivatives and several industry and academic articles. Sébastien received his Ph.D. in Quantitative Finance from Université Paris-Saclay under the guidance of Peter Carr, Stéphane Crépey and Andrew Papanicolaou, and he is also a graduate from The University of Chicago, HEC Paris, Columbia University and Sorbonne Université (fmr. Pierre-et-Marie-Curie).