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Financial markets with small frictions: from individual investors towards equilibria

Titel Englisch Financial markets with small frictions: from individual investors towards equilibria
Gesuchsteller/in Muhle-Karbe Johannes
Nummer 150101
Förderungsinstrument Projektförderung (Abt. I-III)
Forschungseinrichtung Departement Mathematik ETH Zürich
Hochschule ETH Zürich - ETHZ
Hauptdisziplin Volkswirtschaftslehre
Beginn/Ende 01.09.2014 - 31.08.2016
Bewilligter Betrag 203'637.00
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Alle Disziplinen (3)

Disziplin
Volkswirtschaftslehre
Mathematik
Betriebswirtschaftslehre

Keywords (6)

Transaction Costs; Market Frictions; Asymptotics; Equilibrium; Portfolio Choice; Financial Markets

Lay Summary (Deutsch)

Lead
Die klassische Finanzmarkttheorie basiert auf friktionslosem Handeln. Tatsächlich gibt es jedoch selbst in den liquidesten Märkten eine Vielzahl von Friktionen: Bid-Ask Spreads führen zu unterschiedlichen Kauf- und Verkaufspreisen, grosse Käufe oder Verkäufe beeinflussen die Marktpreise, usw. In diesem Projekt soll der Einfluss solcher Marktfriktionen untersucht werden; zunächst für individuelle Investoren und im Anschluss auch für Gleichgewichte zwischen mehreren Akteuren.
Lay summary

Marktfriktionen erlauben neue Blickwinkel auf eine Vielzahl von Fragestellungen in der Finanztheorie, von der Abschätzung von Handelskosten in der Praxis bis hin zu Gleichgewichtmodellen für Preise, Handelsvolumen oder Risikoprämien. In der Tat konnten sich der Nobelpreisträger Paul Krugman und John Cochrane, der Präsident der American Finance Association, in ihrer hitzigen Diskussion über die Zukunft der Finanzökonomie im Hinblick auf die Finanzkrise nur auf einen Punkt einigen: "flaws and frictions" sind für die Finanzmarktmodelle der Zukunft von zentraler Bedeutung.

Modelle mit Friktionen sind jedoch analytisch oft kaum handhabbar. Deshalb sind in der Literatur zunehmend asymptotische Resultate für kleine Friktionen in den Fokus getreten. In jüngster Vergangenheit sind dabei insbesondere explizite Formeln für allgemeine Modelle mit kleinen Transaktionskosten hergeleitet worden.

In diesem Projekt sollen zunächst ähnliche Ergebnisse für andere Friktionen erarbeitet werden, wie z.B. den Preiseinfluss grosser Käufe und Verkäufe. Im Anschluss soll der Fokus auf Gleichgewichtsprobleme gerichtet werden, wie z.B. den Einfluss von Transaktionssteuern auf Marktpreise oder die Interaktion von High-Frequency Händlern und normalen Investoren. 

 

 

 

 

Direktlink auf Lay Summary Letzte Aktualisierung: 03.10.2013

Lay Summary (Englisch)

Lead
Classical financial theory is built on the assumption of frictionless markets. However, small frictions are present even in the most liquid markets: bid-ask spreads lead to different prices for purchases or sales, large orders move market prices, etc. This project strives to understand the impact of such imperfections on the behavior of individual agents and, eventually, also on equilibria between several of them.
Lay summary

Understanding the effects of market frictions helps to shed new light on numerous issues in finance, ranging from the assessment of trading costs by practitioners to equilibrium models for market making, risk premia, and asset pricing puzzles. Indeed, in their heated discussion about where Financial Economics is headed in the wake of the financial crisis, about the only thing 2008 Nobel laureate Paul Krugman and John Cochrane, 2010 President of the American Finance Association, seemed to agree on was the central importance of "flaws and frictions" in models of financial markets.

 Yet, models with frictions have proved to be notoriously intractable. As a way out, there has been increasing emphasis on studying the practically relevant limiting regime of small frictions, to reveal the salient features of the problem while remaining a good approximation to the full but more complicated model. Recently, the scope of this approach has expanded dramatically, leading to explicit asymptotic formulas even in general models with bid-ask spreads.

This project builds on these results. The initial goal is to obtain extensions to other frictions such as price impact of large trades. Then, the plan is to move on to equilibrium problems like the impact of transaction taxes on asset prices, and the interaction between liquidity providers and takers in high-frequency trading.

Direktlink auf Lay Summary Letzte Aktualisierung: 03.10.2013

Verantw. Gesuchsteller/in und weitere Gesuchstellende

Mitarbeitende

Name Institut

Zusammenarbeit

Gruppe / Person Land
Formen der Zusammenarbeit
Dublin City University Irland (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
- Forschungsinfrastrukturen
- Austausch von Mitarbeitern
Osaka University Japan (Asien)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
London School of Economics Grossbritannien und Nordirland (Europa)
- Publikation
Universität Wien Österreich (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
- Forschungsinfrastrukturen
- Austausch von Mitarbeitern
CAU Kiel Deutschland (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
- Forschungsinfrastrukturen
- Austausch von Mitarbeitern

Wissenschaftliche Veranstaltungen

Aktiver Beitrag

Titel Art des Beitrags Titel des Artikels oder Beitrages Datum Ort Beteiligte Personen
Workshop on Stochastic Analysis and Mathematical Finance Vortrag im Rahmen einer Tagung Equilibrum Models with Small Fricitons 25.07.2016 Banff, Kanada Muhle-Karbe Johannes;
Computational Finance Seminar Einzelvortrag Portfolio Choice with Small Nonlinear Price Impact 18.04.2016 Pittsburgh, Vereinigte Staaten von Amerika Muhle-Karbe Johannes;
Financial Mathematics Seminar Einzelvortrag Sensitivity of Optimal Consumption Streams 16.03.2016 Ann Arbor, Vereinigte Staaten von Amerika Herdegen Martin;
Computational Finance Seminar Einzelvortrag Equilibrium Models with Small Transaction Costs 14.03.2016 Pittsburgh, Vereinigte Staaten von Amerika Herdegen Martin;
Vienna Seminar in Mathematical Finance and Probability Einzelvortrag Equilibrium Models with Small Transaciton Costs 14.01.2016 Wien, Österreich Herdegen Martin;
LSE Risk & Stochastics Seminar Einzelvortrag Sensitivity of Optimal Consumption Streams 07.05.2015 London, Grossbritannien und Nordirland Herdegen Martin;
Seminar on Stochastic Analysis and Mathematical Finance Einzelvortrag Sensitivity of Optimal Consumption Streams 16.04.2015 Berlin, Deutschland Herdegen Martin;
Conference of Stochastic Portfolio Theory Vortrag im Rahmen einer Tagung Trading with Small Price Impact 08.03.2015 New York, Vereinigte Staaten von Amerika Muhle-Karbe Johannes;
London Quantitative Finance Seminar Einzelvortrag Trading with Small Price Impact 05.03.2015 London, Grossbritannien und Nordirland Muhle-Karbe Johannes;
SIAM Conference on Financial Mathematics Vortrag im Rahmen einer Tagung Trading with Small Price Impact 13.11.2014 Chicago, Vereinigte Staaten von Amerika Muhle-Karbe Johannes;


Veranstaltungen zum Wissenstransfer

Aktiver Beitrag

Titel Art des Beitrags Titel des Artikels oder Beitrages Datum Ort Beteiligte Personen
Munich Re Summer School on Mathematical Finance Workshop 06.07.2015 Schloss Neutrauchburg, Isny, Deutschland


Abstract

Classical financial theory is built on the assumption of perfectly liquid markets. If prices follow continuous-time diffusions, then this also holds for most optimal trading strategies [Merton (1969, 1971)]. As a result, frictionless models typically prescribe incessant trading, which is unfeasible with even the slightest market imperfections. Among these, proportional transaction costs affect all investors in the form of bid-ask spreads. In addition, small private investors are heavily influenced by fixed fees per transaction, levied upon them by their brokers. Conversely, the transactions of large institutional traders move the quoted market prices, so that the price impact of their transactions becomes a major concern.Understanding the impact of such market frictions helps to shed new light on numerous issues in finance, ranging from the assessment of trading costs by practitioners [Martin and Schöneborn (2011), Martin (2012), Bouchaud et al. (2012), Lehalle et al. (2013)] tractable models for the stylized facts of the trading volume observed on stock exchanges [Epps (1976), Gerhold et al. (2012), Guasoni and Weber (2012)], to equilibrium models for market making [Rosu (2009)], risk premia [Garleanu and Pedersen (2012)], and asset pricing puzzles [Luttmer (1996)]. Indeed, in their heated discussion about where Financial Economics is headed in the wake of the financial crisis, about the only thing 2008 Nobel laureate Paul Krugman and John Cochrane, 2010 President of the American Finance Association, seemed to agree on was the central importance of "flaws and frictions" in models of financial markets.Yet, models with frictions have proved to be notoriously intractable, even in simple concrete settings and for the most tractable optimization problems. As John Cochrane recently put it: "the problem is that we don’t have enough math. [...] Frictions are just bloody hard with the mathematical tools we have now." As a way out, there has been increasing emphasis on studying the practically relevant limiting regime of small frictions, to "reveal the salient features of the problem while remaining a good approximation to the full but more complicated model" [Whalley and Wilmott (1997)]. Very recently, the scope of this approach has expanded dramatically. More specifically, Soner and Touzi (2012) as well as Kallsen and the present author [Kallsen and Muhlekarbe (2012, 2013)] have shown that -- even for general models and optimization problems -- the leading-order corrections for small proportional transaction costs are still of a surprisingly simple form. Indeed, they can typically be computed explicitly as soon as the solution of the frictionless problem is available in closed form. This opens the door to a number of fundamental research questions that constitute the major goals of the present project:Impact of Small Frictions on Individual InvestorsOn the level of individual investors, the goal is to extend the results for proportional costs both to fixed fees and price impact models. In addition, we plan to tackle the combination of proportional costs with either fixed costs or price impact, which are the practically relevant regimes for small private investors or large institutional entities, respectively. Optimal Market Making and Liquidity ProvisionClassical investors have intrinsic motives to trade, e.g., rebalancing their portfolio to maximize its long-run growth rate. As a result, they typically act as "liquidity takers", crossing the bid-ask spread to execute their orders against available counterparties. In contrast, "liquidity providers" stand ready to match such incoming trades. Since this forces them to build up a position they do not want to hold a priori, they are compensated by earning the spread. Until recently, this role was filled by market making "specialists" in most markets. Now, however, the development of computerized limit-order markets has allowed virtually anyone to engage in this endeavor, which in turn has fueled the continued growth of high-frequency trading. The analysis of optimal market making and liquidity provision represents another central goal of the present project.Equilibrium Asset Prices and SpreadsThe subprojects summarized in the previous two paragraphs focus on individual investors, for which asset prices are assumed to be given exogenously. This approach -- commonly adopted in Mathematical Finance -- is appealing due to its analytical tractability. On the other hand, it leads to thorny conceptual issues when trying to discern the impact of policy changes like the introduction of a transaction tax. Such fundamental changes of the playing field in turn affect asset prices and therefore call for the equilibrium models widely used in Financial Economics, where prices are determined endogenously so as to match supply and demand. Then again, most equilibrium models suffer from a severe lack of tractability. Typically, they can only be solved numerically, which calls for computationally intensive numerical analysis and usually does not lead to simple and robust rules of thumb encoding the crucial features of the solution. In the present project, we want to contribute to bridging this gap for models with small frictions. More specifically, the goal is to bring the powerful closed-form asymptotics for individual investors to bear on equilibrium problems, so as to obtain tractable corrections to their frictionless counterparts. Results of this kind will pave the way to assessing how a given exogenous friction changes risk premia and volatilities and -- eventually -- open the door to analyzing the welfare effects of policy changes like the introduction of a transaction tax or the passage from specialist market makers to a limit-order market. A related issue is how frictions, e.g. bid-ask spreads, themselves arise in equilibrium. This is another focal topic that we expect to address, both for primary securities like stocks and for derivatives written on them. In doing so, we hope to shed new light on the welfare distribution between liquidity takers and providers, and links between the liquidity for stocks and options written on them.
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