BACHELIER FINANCE SOCIETY ONE WORLD SEMINARS (ONLINE)
Started during the pandemic, we want to keep the active spirit of our whole scientific community going and to continue solving financial problems of our times and keep our online seminars going.
We organise an online talk on the last Thursday of a month (with a few exceptions), alternating with the talks set up by the SIAM activity group on financial mathematics and engineering (http://wiki.siam.org/siag-fm/index.php/Current_events).
Find the list of the BFS One World Seminars below.
2024
Dates for 2025 will be published when available.
Date: Thursday, 28 November 2024
Speaker: Giorgia Callegaro (U. Padova)
Title: Continuous-time persuasion by filtering
Abstract: We frame dynamic persuasion in a partial observation stochastic control game with an ergodic criterion. The Receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the Receiver through a device designed by the Sender that generates the observation process. The commitment of the Sender is enforced. We develop this approach in the case where all dynamics are linear and the preferences of the Receiver are linear-quadratic. We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the Receiver’s value function. An extension to the case of persuasion of a mean field of interacting Receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that when firms declare a high level of best-in-class target, the information provided by stringent accounting rules offsets the Nash equilibrium effect that leads firms to increase pollution to make their target easier to achieve.
This is a joint work with: R. Aid, O. Bonesini and L. Campi.
Thursday, 28 November 2024, 19:00 (GMT +1)
Slides to talk:
slides_callegaro_241128
Date: Thursday, 24 October 2024
Speaker: Johannes Wiesel (Carnegie Mellon University)
Title: Bounding adapted Wasserstein metrics
Abstract: The Wasserstein distance \(\mathcal{W}_p\) is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years. The adapted Wasserstein distance \(\mathcal{A}\mathcal{W}_p\) extends this theory to laws of discrete time stochastic processes in their natural filtrations, making it particularly well suited for analyzing time-dependent stochastic optimization problems.
While the topological differences between \(\mathcal{A}\mathcal{W}_p\) and \(\mathcal{W}_p\) are well understood, their differences as metrics remain largely unexplored beyond the trivial bound \(\mathcal{W}_p\le \mathcal{A}\mathcal{W}_p\). This paper closes this gap by providing upper bounds of \(\mathcal{A}\mathcal{W}_p\) in terms of \(\mathcal{W}_p\) through investigation of the smooth adapted Wasserstein distance. Our upper bounds are explicit and are given by a sum of \(\mathcal{W}_p\), Eder’s modulus of continuity and a term characterizing the tail behavior of measures. As a consequence, upper bounds on \(\mathcal{W}_p\) automatically hold for \(\mathcal{AW}_p\) under mild regularity assumptions on the measures considered. A particular instance of our findings is the inequality \(\mathcal{A}\mathcal{W}_1\le C\sqrt{\mathcal{W}_1}\) on the set of measures that have Lipschitz kernels.
Our work also reveals how smoothing of measures affects the adapted weak topology. In fact, we find that the topology induced by the smooth adapted Wasserstein distance exhibits a non-trivial interpolation property, which we characterize explicitly: it lies in between the adapted weak topology and the weak topology, and the inclusion is governed by the decay of the smoothing parameter.
This talk is based on joint work with Jose Blanchet, Martin Larsson and Jonghwa Park.
Thursday, 24 October 2024, 19:00 (GMT +2)
Slides to talk:
slides_wiesel_241024
Date: Thursday, 26 September 2024
Speaker: Sara Biagini (LUISS University)
Title: Carbon neutrality and net-zero in compliance markets
Abstract: When addressing climate risk mitigation, a primary objective is achieving climate neutrality. We analyze first the impact of carbon neutrality policies on a system of polluting companies that are regulated within an ETS carbon market. The companies are mandated to cut emissions and have the option to trade carbon allowances for compliance purposes. They may also be allocated additional allowances as subsidies from the regulatory authority to assist in fulfilling compliance. For each firm, the key variable is the imbalance between their cumulative Business As Usual emissions and the allocation they may receive, which must be covered by the regulated maturity.
For a given subsidy scheme, a unique, closed-form equilibrium is reached. The resulting allowances price admits a neat expression as a convex combination of each company’s marginal costs, each calculated based on their predicted emissions imbalance. In turn, each company’s cost-minimizing abatement and trade strategies admit an intuitive decomposition in terms of their emissions imbalance and the equilibrium price. The model is quite flexible and allows exploration of the effect of various policies, according to the additional priorities of the regulator. The more ambitious net-zero goal is obtained as a special case. Companies cannot benefit from carbon allowances and they must effectively neutralize all their carbon footprint. The cost minimization problem is now at the individual company level, and we present a closed-form solution for optimal reduction. All results are illustrated with numerical examples.
Thursday, 26 September 2024, 19:00 (GMT +2)
Date: Thursday, 27 June 2024
Speaker: Alvaro Cartea (University of Oxford)
Title: Spoofing and Manipulating Order Books with Learning Algorithms
Abstract: We propose a dynamic model of the limit order book to derive conditions to test if a trading algorithm will learn to manipulate the order book. Our results show that as a market maker becomes more tolerant to bearing inventory risk, the learning algorithm will find optimal strategies that manipulate the book more frequently. Manipulation occurs to induce mean reversion in inventory to an optimal level and to execute round-trip trades with limit orders at a higher probability than was otherwise likely to occur; spoofing is a special case when the market maker prefers that manipulative limit orders are not filled. The conditions are tested with order book data from Nasdaq and we show that market conditions are conducive for an algorithm to learn to manipulate the order book. Finally, when two market makers use learning algorithms to trade, their algorithms can learn to coordinate their manipulation.
Joint work with Patrick Chang and Gabriel García-Arenas.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4639959
Thursday, 27 June 2024, 19:00 (GMT +2)
Date: Thursday, 23 May 2024
Speaker: Samuel Cohen (University of Oxford)
Title: Calibration of Hawkes-like processes for LOBs
Abstract: One of the common families of models for high-frequency data is self-exciting processes, such as Hawkes processes. Except in the memoryless case, these processes are generally not Markov, and their calibration to data is delicate and computationally challenging. In this talk we will explore a gradient-descent algorithm for calibration, which allows for a wide variety of models to be considered. We will also apply this to limit-order-book data, and see that some of the classic ‘stylized fact’ of these models may be simply due to artifacts of calibration.
Thursday, 23 May 2024, 19:00 (GMT +2)
Date: Thursday, 25 April 2024
Speaker: Johannes Ruf (LSE)
Title: The numeraire e-variable and reverse information projection
Abstract: We consider testing a composite null hypothesis \(\mathcal{P}\) against a point alternative \(\mathsf{Q}\) using e-variables, which are nonnegative random variables \(X\) such that \(\mathbb{E}_\mathsf{P}[X] \leq 1\) for every \(\mathsf{P} \in \mathcal{P}\). This paper establishes a fundamental result: under no conditions whatsoever on \(\mathcal{P}\) or \(\mathsf{Q}\), there exists a special e-variable \(X^*\) that we call the numeraire, which is strictly positive and satisfies \(\mathbb{E}_\mathsf{Q}[X/X^*] \leq 1\) for every other e-variable \(X\). In particular, \(X^*\) is log-optimal in the sense that \(\mathbb{E}_\mathsf{Q}[\log(X/X^*)] \leq 0\). Moreover, \(X^*\) identifies a particular sub-probability measure \(\mathsf{P}^*\) via the density \(d \mathsf{P}^*/d \mathsf{Q} = 1/X^*\). As a result, \(X^*\) can be seen as a generalized likelihood ratio of \(\mathsf{Q}\) against \(\mathcal{P}\). We show that \(\mathsf{P}^*\) coincides with the reverse information projection (RIPr) when additional assumptions are made that are required for the latter to exist. Thus \(\mathsf{P}^*\) is a natural definition of the RIPr in the absence of any assumptions on \(\mathcal{P}\) or \(\mathsf{Q}\). In addition to the abstract theory, we provide several tools for finding the numeraire and RIPr in concrete cases. We discuss several nonparametric examples where we can indeed identify the numeraire and RIPr, despite not having a reference measure. Our results have interpretations outside of testing in that they yield the optimal Kelly bet against \(\mathcal{P}\) if we believe reality follows \(\mathsf{Q}\).
Joint work with Martin Larsson and Aaditya Ramdas
Thursday, 25 April 2024, 19:00 (GMT +2)
Slides to talk:
slides_ruf_240425
Date: Thursday, 21 March 2024
Speaker: Daniel Lacker (Columbia University)
Title: Non-asymptotic perspectives on mean field approximations and stochastic control
Abstract: The main focus of this talk is the analysis of high-dimensional stochastic control problems in which many agents cooperate to minimize a convex cost functional. Our main results are sharp yet general bounds on the optimality gap between the full-information problem, in which each agent observes the states of all other agents, versus the distributed problem, in which each agent observes only its own state. Being decidedly non-asymptotic, our approach avoids structural constraints like exchangeability which are normally required in order to identify limiting objects, but which rule out network-based models. A protagonist in our approach, dubbed the “independent projection,” is the optimal approximation (in a precise sense) of a given high-dimensional diffusion process by one in which the coordinates are independent. Based in part on joint works with Sumit Mukherjee and Lane Chun Yeung, and with Joe Jackson.
Thursday, 21 March 2024, 19:00 (GMT +1)
Slides to talk:
slides_lacker_240321
Date: Thursday, 22 February 2024
Speaker: Carole Bernard (Grenoble Ecole de Management)
Title: Multivariate Portfolio Choice via Quantiles
Abstract: We first show how the quantile approach used for univariate optimal portfolio choice can be also useful to solve the multivariate case. When the multivariate risk sharing problem (in the absence of a financial market) can be solved explicitly, the multivariate optimal portfolio choice reduces to a one-dimensional problem using the quantile approach. In the general case, we develop a numerical approach to obtain approximate solutions for the multivariate optimal portfolio selection problem. In the case of an optimization of a sum of distortion risk measures (e.g., RVaR) we discuss optimal explicit solutions of the multivariate portfolio choice.
Joint work with Andrea Perchiazzo and Steven Vanduffel
Thursday, 22 February 2024, 19:00 (GMT +1)
Slides to talk:
slides_bernard_240222
Date: Thursday, 25 January 2024
Speaker: Marcel Nutz (Columbia University)
Title: Unwinding Stochastic Order Flow: When to Warehouse Trades
Abstract: We study how to unwind stochastic order flow with minimal transaction costs. Stochastic order flow arises, e.g., in the central risk book (CRB), a centralized trading desk that aggregates order flows within a financial institution. The desk can warehouse in-flow orders, ideally netting them against subsequent opposite orders (internalization), or route them to the market (externalization) and incur costs related to price impact and bid-ask spread. We model and solve this problem for a general class of in-flow processes, enabling us to study in detail how in-flow characteristics affect optimal strategy and core trading metrics. Our model allows for an analytic solution in semi-closed form and is readily implementable numerically. Compared with a standard execution problem where the order size is known upfront, the unwind strategy exhibits an additive adjustment for projected future in-flows. Its sign depends on the autocorrelation of orders; only truth-telling (martingale) flow is unwound myopically. In addition to analytic results, we present extensive simulations for different use cases and regimes, and introduce new metrics of practical interest. (Joint work with Kevin Webster and Long Zhao; preprint available at https://ssrn.com/abstract=4609588)
Thursday, 25 January 2024, 19:00 (GMT +1)
Slides to talk:
slides_nutz_240125
