Research

Evolutionary dynamics of international currencies & non-sovereign assets

Collaborators' institutions: Banque de France

A stochastic evolutionary model of the hazard rate of transitions between global currency regimes. It tracks how decentralised agents coordinate on the unit-of-account, medium-of-exchange and store-of-value functions, and maps metastable shifts between the dollar-centred equilibrium, sovereign challengers, and non-sovereign assets such as gold and Bitcoin.

Factorial strategy based on the cross section of crypto returns

Collaborators' institutions: UCL · ESILV

Statistical factors in the cross-section of cryptocurrency returns, including on-chain metrics and continuous-trading variables, tested out of sample to separate the signals that hold from the factor zoo, and the portfolio strategies built on them.

Option pricing across closed trading windows

Collaborators' institutions: CAAN · ESILV

As equities move towards continuous trading, listed options remain restricted to regular hours, which changes how variance accumulates and how intraday risk is priced. With no equity history of continuous trading, the paper builds an empirical proxy from IBIT, Deribit and Bitcoin data.

Execution cost and margin allocation for crypto trading agents

Collaborators' institutions: QVANTS · ESILV

Two costs that autonomous agents on perpetual markets rarely measure: the lifetime cost of a position, execution slippage plus funding, which can erase a strategy's expected profit; and the correlation created when independent agents share collateral, which concentrates exposure and can trigger the liquidation of the shared account.

An equity-implied rating model for unrated firms ↗

Journal of Computational Finance

Collaborators' institutions: EthiFinance

While investors and lenders rely on one or more external credit rating agencies (eg, S&P, Moody’s or Fitch Ratings) to directly assess their obligors’ credit quality, or simply to benchmark their own estimates, part of their portfolio might not be covered by these credit assessment institutions. Consequently, some practitioners estimate obligors’ probability of default using models derived from Merton’s classic 1974 model and then translate them into market-implied ratings. These measures are highly volatile and sensitive to overall market movement; that is, probabilities of default are high in a bear market and low in a bull market, whereas an obligor’s actual credit quality might stay relatively stable. In this paper we propose an alternative approach based on Merton’s distance to default. We compute the distance to default from market data and transform it into a distance-to-default-based rating for each firm listed on the stock market. Further, we use a machine learning algorithm to link the firm’s distance to default and sector to its credit rating. Ultimately, this approach allows us to assign a distance-to-default-based rating to unrated firms. To show the relevance of this method, we compare the explanatory power of the model’s equity-implied ratings with those of actual credit ratings in relation to the interest/debt ratio, and we find similar results (ie, a coefficient of determination of 87% in both cases). This demonstrates that our model explains the interest rates paid as well as the credit ratings.

The environmental cost of Bitcoin and PoW cryptos: analyzing their energy consumption and carbon emissions ↗

ResearchGate

Collaborators' institutions: EthiFinance

This report presents a methodology for calculating the electricity consumption and associated carbon emissions of Proof of Work (PoW) cryptocurrencies, focusing primarily on Bitcoin. We analyse electricity usage by examining network hashrates, mining hardware efficiency, and auxiliary factors affecting power usage effectiveness. Additionally, we assess the carbon footprint by considering the geographical distribution of mining operations and the regional carbon intensity of power generation. The findings offer a detailed insight into the environmental impact of PoW cryptocurrencies, contributing to the discourse on their sustainability and guiding informed decision-making in cryptocurrency mining practices.

Universal hidden monotonic trend estimation with contrastive learning ↗

Intelligent Computing, Springer

Collaborators' institutions: EthiFinance · Safran

In this paper, we describe a universal method for extracting the underlying monotonic trend factor from time series data. We propose an approach related to the Mann-Kendall test, a standard monotonic trend detection method and call it contrastive trend estimation (CTE). We show that the CTE method identifies any hidden trend underlying temporal data while avoiding the standard assumptions used for monotonic trend identification. In particular, CTE can take any type of temporal data (vector, images, graphs, time series, etc.) as input. We finally illustrate the interest of our CTE method through several experiments on different types of data and problems.

Data-driven modeling of the temporal evolution of breakers’ states in the French electrical transmission grid ↗

Nonlinear Analysis: Hybrid Systems

Collaborators' institutions: CNRS · CentraleSupélec

In electrical transmission grids, it is common to observe the states of circuit breakers. While they are known at irregular times, system modeling and grid state estimation are of the highest importance to ensure secure operations. This paper proposes a richer method to estimate the grid state over its reference configurations based on the temporal evolution of its breakers’ states. The first contribution consists in developing a general multi-observation continuous-time finite-state Hidden Markov Model with filter-based parameter estimation to infer the hidden state (e.g., the grid reference configuration) handling multiple observed processes with irregular “jump” times (e.g., the breakers’ states). As a second contribution, we build a numerical scheme with no discretization error adapted to all state jumps generated by the observed processes. Finally, we apply our model to simulated and real data to illustrate the approach’s performance. The available data consists of historical records of breakers’ states during the electrical transmission grid operated normally. For this real-data-driven application, we also present a clustering approach to identify the set of grid reference configurations.

Optimal hedging of French savings products ↗

ResearchGate

Collaborators' institutions: EthiFinance

The Livret de Développement Durable et Solidaire (LDDS) and the Livret A are French regulated savings products. The financial institutions that offer them must remunerate savers at a rate set by a formula. In return, the savings deposits are invested, generally in fixed-rate loans, the rate of which can be exchanged for a variable rate and/or hedged against inflation using swaps. The allocation of the savings deposits on loans or swaps is called a hedging convention. For asset-liability management (ALM) service providers, the question is: how do we find the optimal hedging convention? The difficulty behind this problem is the need to plug together ALM and portfolio management models. In this paper, we propose a proper formalization of the problem, considering the practical requirements of ALM. We also illustrate our method with experiments and show how it can be used to appraise the importance of certain assumptions represented by parameters of the hedging problem.

Distributed power consumption scheduling ↗

Advanced Data Analytics for Power Systems, Cambridge University Press

Collaborators' institutions: CNRS · EDF

This chapter studies the impact of the deployment of electric vehicles (EVs) at a large scale on the existing and future energy networks. The impact on the grid is assessed in terms of residential distribution network (DN) costs. Essentially, the main goal to optimize the battery charging schedules of EVs to minimize a cost that takes into account residential distribution transformer aging and the distribution energy losses. Within this context, the underlying mathematical tool is a static noncooperative game that describes the interaction between all EVs and the DN operator. An equilibrium analysis is conducted for this game in both its atomic and nonatomic versions.

A continuous-time hidden Markov model of credit quality underlying published agencies' ratings ↗

ResearchGate

Collaborators' institutions: EthiFinance

In credit quality assessment, it is common to have a group of debt issuers for which we observe one or several ratings given by agencies (e.g., Standard & Poor's, Moody's, Fitch). Generally, a way to summarize several observed ratings into one credit quality rating is to average them. In this paper, we propose a richer method to infer the credit quality underlying a group of observed ratings. As a first contribution, we formalize the problem by adapting a Continuous-Time Hidden Markov Model (CT-HMM) such that it handles multiple observed ratings with irregular publication dates. Our second contribution consists in building adapted finite-dimensional filters and an ad-hoc numerical method with no discretization error to infer the maximum-likelihood hidden rating from the observed ratings. Finally, we perform a set of experiments on both simulated and real sovereign credit ratings to illustrate the interest of our approach.

Stochastic games on graphs with applications to smart-grids optimization ↗

ERC-funded project EQUALIS

Collaborators' institutions: CNRS · ENS · CentraleSupélec

This thesis applies formal methods, game theory and optimisation to energy grids, where both correctness and optimality are required. It focuses on power consumption scheduling: each consumer, such as an electric vehicle owner, must reach a target energy level before a deadline by choosing a consumption power over time. Centralised designs, with a single decision-maker, and decentralised ones, with one decision-maker per consumer, are both analysed. The problem is modelled with Markov decision processes and stochastic games, where probabilities represent the non-controllable consumption, and strategies are designed to be functionally correct and robust against changes of the environment.

Optimization under probability constraints and controlled Markov processes ↗

GRETSI XXVII

Collaborators' institutions: CNRS · CentraleSupélec · ENS

This article focuses on the existence and synthesis of strategies in double-weighted Markov decision processes, which satisfy both a probability constraint over a weighted reachability condition, and a quantitative constraint on the expected value of a random variable defined using another reachability condition. This work generalizes a scheduling problem for energy consumption (typically the problem of charging electric vehicles). We study the set of values of a parameter (a threshold) for which the problem has a solution, and show how a partial characterization of this set can be obtained via two sequences of optimization problems. We also discuss the completeness and feasibility of the resulting approach.

Multi-weighted Markov decision processes with reachability objectives ↗

Electronic Proceedings in Theoretical Computer Science

Collaborators' institutions: CNRS · ENS · FNRS · UMONS

We are interested in the synthesis of schedulers in double-weighted Markov decision processes, which satisfy both a percentile constraint over a weighted reachability condition, and a quantitative constraint on the expected value of a random variable defined using a weighted reachability condition. This problem is inspired by the modelization of an electric-vehicle charging problem. We study the cartography of the problem, when one parameter varies, and show how a partial cartography can be obtained via two sequences of opimization problems. We discuss completeness and feasability of the method.

Energy consumption scheduling strategies with imperfect forecasting information ↗

GRETSI XXVI

Collaborators' institutions: CNRS · ENS · CentraleSupélec · EDF

Energy consumption problems (e.g., electric vehicles charging) are very related to communication problems. The “water-filling” algorithm can be used, but it is not robust w.r.t. the noise of the “non-flexible”, i.e. not controllable, energy consumption forecasting. We propose a robust algorithm using the probabilistic model checker PRISM, to exploit the idea of discretizing the consumption action (as for a modulation to small constellation) and the dynamic structure of the problem in a Markov decision process model.