Olivier Gueant

Olivier Gueant
École Nationale de la Statistique et de l'Administration Économique | ENSAE · Crest

About

62
Publications
26,358
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1,868
Citations
Citations since 2016
24 Research Items
1328 Citations
2016201720182019202020212022050100150200
2016201720182019202020212022050100150200
2016201720182019202020212022050100150200
2016201720182019202020212022050100150200

Publications

Publications (62)
Preprint
Full-text available
Modern portfolio theory has provided for decades the main framework for optimizing portfolios. Because of its sensitivity to small changes in input parameters, especially expected returns, the mean-variance framework proposed by Markowitz (1952) has however been challenged by new construction methods that are purely based on risk. Among risk-based...
Preprint
Full-text available
In FX cash markets, market makers provide liquidity to clients for a wide variety of currency pairs. Because of flow uncertainty and market volatility, they face inventory risk. To mitigate this risk, they typically skew their prices to attract or divert the flow and trade with their peers on the dealer-to-dealer segment of the market for hedging p...
Preprint
Full-text available
Dealers make money by providing liquidity to clients but face flow uncertainty and thus price risk. They can efficiently skew their prices and wait for clients to mitigate risk (internalization), or trade with other dealers in the open market to hedge their position and reduce their inventory (externalization). Of course, the better control associa...
Preprint
Full-text available
In OTC markets, one of the main tasks of dealers / market makers consists in providing prices at which they agree to buy and sell the assets and securities they have in their scope. With ever increasing trading volume, this quoting task has to be done algorithmically. Over the last ten years, many market making models have been designed that can be...
Preprint
Full-text available
In recent years, academics, regulators, and market practitioners have increasingly addressed liquidity issues. Amongst the numerous problems addressed, the optimal execution of large orders is probably the one that has attracted the most research works, mainly in the case of single-asset portfolios. In practice, however, optimal execution problems...
Article
A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functions of many multi-asset extens...
Preprint
For optimal control problems on finite graphs in continuous time, the dynamic programming principle leads to value functions characterized by systems of nonlinear ordinary differential equations. In this paper, we exhibit a family of such optimal control problems for which these nonlinear equations can be transformed into linear ones thanks to a ch...
Article
In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an option market maker is in fact tractable. More precisely, when volatility i...
Article
In most over‐the‐counter (OTC) markets, a small number of market makers provide liquidity to other market participants. More precisely, for a list of assets, they set prices at which they agree to buy and sell. Market makers face therefore an interesting optimization problem: They need to choose bid and ask prices for making money while mitigating...
Preprint
In this paper, we address the question of the optimal Delta and Vega hedging of a book of exotic options when there are execution costs associated with the trading of vanilla options. In a framework where exotic options are priced using a market model (e.g. a local volatility model recalibrated continuously to vanilla option prices) and vanilla opt...
Article
When firms want to buy back their own shares, they have a choice between several alternatives. If they often carry out open market repurchase, they also increasingly rely on banks through complex buyback contracts involving option components, e.g. accelerated share repurchase contracts, VWAP-minus profit-sharing contracts, etc. The entanglement bet...
Article
In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for bonds to asset managers. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. The existing models, mostly inspired by the Avellaneda-Stoikov model, descr...
Article
Full-text available
The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In particular, we provide results on the long-term behavior of value functions and optimal controls, along with res...
Preprint
In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for a large number of bonds to asset managers from all around the globe. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. Useful models exist, most of th...
Article
Full-text available
This paper presents several models addressing optimal portfolio choice, optimal portfolio liquidation, and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling between Bayesian learning and dynamic programming techniques that leads to partial differential equations. It e...
Preprint
Full-text available
In this article, we tackle the problem of a market maker in charge of a book of equity derivatives on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an equity option market maker is in fact tractable. More precisely,...
Preprint
When firms want to buy back their own shares, they have a choice between several alternatives. If they often carry out open market repurchase, they also increasingly rely on banks through complex buyback contracts involving option components, e.g. accelerated share repurchase contracts, VWAP-minus profit-sharing contracts, etc. The entanglement bet...
Preprint
Full-text available
In most OTC markets, a small number of market makers provide liquidity to clients from the buy side. More precisely, they set prices at which they agree to buy and sell the assets they cover. Market makers face therefore an interesting optimization problem: they need to choose bid and ask prices for making money out of their bid-ask spread while mi...
Article
In most illiquid markets, there is no obvious proxy for the market price of an asset. The European corporate bond market is an archetypal example of such an illiquid market where mid-prices can only be estimated with a statistical model. In this OTC market, dealers/market makers only have access, indeed, to partial information about the market. In...
Preprint
The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In particular, we provide results on the long-term behavior of value functions and optimal controls, along with res...
Preprint
In most illiquid markets, there is no obvious proxy for the market price of an asset. The European corporate bond market is an archetypal example of such an illiquid market where mid-prices can only be estimated with a statistical model. In this OTC market, dealers / market makers only have access, indeed, to partial information about the market. I...
Article
This paper presents several models addressing optimal portfolio choice and optimal portfolio transition issues, in which the expected returns of risky assets are unknown. Our approach is based on a coupling between Bayesian learning and dynamic programming techniques. It permits to recover the well-known results of Karatzas and Zhao in the case of...
Article
Market makers provide liquidity to other market participants: they propose prices at which they stand ready to buy and sell a wide variety of assets. They face a complex optimization problem with static and dynamic components: they need indeed to propose bid and offer/ask prices in an optimal way for making money out of the difference between these...
Article
Full-text available
The ad-trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey auctions -- throughout the day for buying ad-inventory with the aim of maximizing one or several key performance indicators (...
Article
For the last two decades, most financial markets have undergone an evolution toward electronification. The market for corporate bonds is one of the last major financial markets to follow this unavoidable path. Traditionally quote-driven (that is, dealer-driven) rather than order-driven, the market for corporate bonds is still mainly dominated by vo...
Article
Be it for taking advantage of stock undervaluation or in order to distribute part of their profits to shareholders, firms may buy back their own shares. One of the way they proceed is by including Accelerated Share Repurchases (ASR) as part of their repurchase programs. In this article, we study the pricing and optimal execution strategy of an ASR...
Article
Full-text available
In spite of the growing consideration for optimal execution issues in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to approximate the optimal strategy of a trader willing to unwind a large portfolio. The method we propose is very g...
Article
Full-text available
In this article, we consider a specific optimal execution problem associated to accelerated share repurchase contracts. When firms want to repurchase their own shares, they often enter such a contract with a bank. The bank buys the shares for the firm and is paid the average market price over the execution period, the length of the period being dec...
Article
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in a frictionless market, traders cannot be perfectly hedged because of execution costs and market impact. They...
Chapter
Mean field games models describing the limit case of a large class of stochastic differential games, as the number of players goes to +∞, were introduced by Lasry and Lions [C R Acad Sci Paris 343(9/10) (2006); Jpn. J. Math. 2(1) (2007)]. We use a change of variables to transform the mean field games equations into a system of simpler coupled parti...
Article
Full-text available
Optimal liquidation using volume weighted average price (VWAP) strategies has been considered in the literature, though never in the presence of permanent market impact and only rarely with execution costs. Moreover, only VWAP strategies have been studied, and the pricing of guaranteed VWAP contracts has never been addressed. In this article, we de...
Article
There are two schools of thought regarding market impact modeling. On the one hand, seminal papers by Almgren and Chriss introduced a decomposition between a permanent market impact and a temporary (or instantaneous) market impact. This decomposition is used by most practitioners in execution models. On the other hand, recent research advocates for...
Article
The agency problem between an investor and his mutual funds managers has long been studied in the economic literature. Because the very business of mutual funds managers is not only to manage money but also, and rather, to increase the money under management, one of the numerous agency problems is the implicit incentive induced by the relationship...
Article
Full-text available
When executing their orders, investors are proposed different strategies by brokers and investment banks. Most orders are executed using VWAP algorithms. Other basic execution strategies include POV (also called PVol) -- for percentage of volume --, IS -- implementation shortfall -- or Target Close. In this article dedicated to POV strategies, we d...
Article
In this article, we develop a general CARA framework to study optimal execution and to price block trades. We prove existence and regularity results for optimal liquidation strategies under very general hypotheses, and we provide a hamiltonian characterization for the optimal strategy. We then focus on the important topic of block trade pricing and...
Article
Mean field games have been introduced by J.-M. Lasry and P.-L. Lions as the limit case of stochastic differential games when the number of players goes to +∞. In the case of quadratic costs, we present two changes of variables that allow to transform the mean field games (MFG) equations into two simpler systems of equations. The first change of var...
Article
The classical literature on optimal liquidation, rooted in Almgren-Chriss models, tackles the optimal liquidation problem using a trade-off between market impact and price risk. Therefore, it only answers the general question of the optimal liquidation rhythm. The very question of the actual way to proceed with liquidation is then rarely dealt with...
Article
Full-text available
This article discusses the discount rate to be used in projects that aimed at improving the environment. The model has two different goods, one is the usual consumption good whose production may increase exponentially, the other is an environmental good whose quality remains limited. The stylized world we describe is fully determined by four parame...
Chapter
With the rise of electronification and trading automation, the task of quoting assets on many financial markets must be carried out algorithmically by market makers. Market making models and algorithms have therefore been an important research topic in recent years, at the frontier between economics, quantitative finance, scientific computing, and...
Article
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced by J.M. Lasry and P.L. Lions and adapting them to games on graphs, we introduce a partial differentia...
Article
This paper presents a general existence and uniqueness result for the mean field games equations on a graph ($\mathcal{G}$-MFG). In particular, our setting allows to take into account congestion effects as those initially evoked in a continuous framework or even non-local forms of congestion. These general congestion effects are particularly releva...
Article
Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to +∞, have been introduced by J.-M. Lasry and P.-L. Lions in [11, 12, 13]. We use a change of variables to transform the mean field games (MFG) equations into a system of simpler coupled partial differential equations, in t...
Article
Full-text available
This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss, or only on the liquidity-consuming orders like Obizhaeva and Wang, we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order boo...
Article
Full-text available
Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we con...
Chapter
First, the agent-based models [5] aiming at simulating a large number of agents, each of them having its utility function or feedback rule. The philosophy of this kind of modelling is similar to Minsky’s paradigm in artificial intelligence in the eighties: build each agent so that if you stealthily replace, one by one, each real person interacting...
Article
This text is inspired from a “Cours Bachelier” held in January 2009 and taught by Jean-Michel Lasry. This course was based upon the articles of the three authors and upon unpublished materials they developed. Proofs were not presented during the conferences and are now available. So are some issues that were only rapidly tackled during class.
Chapter
Full-text available
In this article we study a decoupled forward backward stochastic differential equation (FBSDE) and the associated system of partial integro-differential obstacle problems, in a flexible Markovian set-up made of a jump-diffusion with regimes. These equations are motivated by numerous applications in financial modeling, whence the title of the paper....
Chapter
Full-text available
This set of lecture notes is concerned with the following pair of ideas and concepts: 1. The Skorokhod Embedding problem (SEP) is, given a stochastic process X=(X t ) t≥0 and a measure μ on the state space of X, to find a stopping time τ such that the stopped process X τ has law μ. Most often we take the process X to be Brownian motion, and μ to...
Chapter
Full-text available
These lecture notes cover a major part of the crash course on financial modeling with jump processes given by the author in Bologna on May 21–22, 2009. After a brief introduction, we discuss three aspects of exponential Lévy models: absence of arbitrage, including more recent results on the absence of arbitrage in multidimensional models, propertie...
Chapter
In this first chapter, we show that a CDO tranche payoff can be perfectly replicated with a self-financed strategy based on the underlying credit default swaps. This extends to any payoff which depends only upon default arrivals, such as basket default swaps. Clearly, the replication result is model dependent and relies on two critical assumptions....
Chapter
This text is inspired from a “Cours Bachelier” held in January 2009 and taught by Jean-Michel Lasry. This course was based upon the articles of the three authors and upon unpublished materials they developed. Proofs were not presented during the conferences and are now available. So are some issues that were only rapidly tackled during class.
Article
In this article, we present a reference case of mean field games. This case can be seen as a reference for two main reasons. First, the case is simple enough to allow for explicit resolution: Bellman functions are quadratic, stationary measures are normal and stability can be dealt with explicitly using Hermite polynomials. Second, in spite of its...
Article
Full-text available
This article discusses the interaction between economic growth in the sense of human capital accumulation and the dynamics of inequalities. We use a mean-field game framework in which individuals improve their human capital both to improve their wages and to avoid potential competition with less skilled individuals. Our contribution is twofold. Fir...
Conference Paper
Full-text available
This article discusses the discount rate to be used in projects that aimed at improving the environment. The model is quite stylized and involves two different goods, one is the usual consumption good whose production increases exponentially, the other is an environmental good whose quality remains limited. We define an ecological discount rate and w...
Article
Sujet proposé par Thierry Lévy, initialement intitulé "Mesures gaussiennes et espaces de Fock". 24 juin 2004 Résumé Les pages qui suivent sont consacrées à un théorème d'Irving Segal donnant une décompo-sition de certains espaces L 2 en somme directe orthogonale d'espaces vectoriels appelés chaos de Wiener. La décomposition hilbertienne classique d...
Article
Directeur de mémoire : Mme Gabrielle Demange 2007 1 Un remerciement va à ceux qui ont eu l'obligence de supporter ma mauvaise humeur estivale, notamment Jean-Michel et Laura Lasry, Edward Chaffetz et Jérôme Lebuchoux.
Article
Le fichier attaché comporte p.16-44 un WP de Roger Guesnerie intitulé "Calcul économique et développement durable" n° 2004-2, WP du DELTA Cet article consiste en un approfondissement de la notion de taux d’intérêt écologique introduite par Roger Guesnerie au début des années 2000. Si nous nous inscrivons dans une parfaite filiation avec Roger Guesne...

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