Thomas Cayé

Department of Mathematics

ETH Zurich

I am currently PhD student in the Stochastic Finance Group in the department of mathematics at ETH Zürich, under the supervision of Prof. Johannes Muhle-Karbe and Prof. Mete Soner. I received my masters from ETH and University Zürich and hold the Diplome d'Ingénieur from Ecole Polytechnique.

Research

Research Interests

  • Mathematical Finance
  • Market Frictions: Nonlinear Price Impact and Proportional Transaction costs
  • Utility Maximization Problems
  • Stochastic Calculus
  • Duality Methods and Stochastic Optimal Control
  • Discrete, Convex, Mixed Optimization
  • Articles Published in peer-reviewed journals

    Liquidation with self-exciting price impact, Thomas Cayé, Johannes Muhle-Karbe
    We study optimal execution with “self-exciting” price impact, where persistent trades not only incur price impact but also increase the execution costs for successive orders. This model is motivated by an equilibrium between fundamental sellers, market makers, and end users. For risk-neutral investors, it leads to faster initial trading compared to the constant execution rate of Bertsimas and Lo. For risk-averse liquidation as in Almgren and Chriss or Huberman and Stanzl, self-excitement has a moderating effect: slow liquidation is sped up, whereas fast schedules are slowed down.
    Link to the SSRN preprint

    Preprints and Working Papers

    Trading with Small Nonlinear Price Impacts, Thomas Cayé, Martin Herdegen, Johannes Muhle-Karbe
    We study portfolio choice with nonlinear price impact in a general setting. Using probabilistic techniques, we show that the asymptotic solution for small impact can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we study how hedging strategies and active portfolio management are affected by the nonlinear trading cost, and also discuss how to endogenize it in an equilibrium between risk-averse clients and dealers.

    Past Talks

  • Financial Mathematics Seminar, DCU, February 2017, Dublin (Ireland), Trading with Small Nonlinear Price Impact
  • Bachelier Colloquium 2017, January 2017, Métabief (France), Trading with Small Nonlinear Price Impact
  • Workshop on Mathematical Finance for young reasercher,, June 2016, Berlin (Germany), Trading with Small Nonlinear Price Impact
  • Post/Doctoral Seminar in Mathematical Finance, Zurich, 19.04.2016, Portfolio Choice with Nonlinear Transaction Cost and Stochastic Investment Opportunities
  • Bachelier Colloquium 2016, January 2016, Métabief (France), Nonlinear Transaction Costs, Portfolio Choice, and Time-varying Investment Opportunities
  • Post/Doctoral Seminar in Mathematical Finance, Zürich, 24.02.2015, Nonlinear Transaction Costs, Portfolio Choice, and Time-varying Investment Opportunities
  • 11th Doktorandentreffen Stochastik,, Berlin (Germany), August 2015, Mean-Variance trading optimization with Small Nonlinear Price Impacts
  • Imperial College-ETH Workshop on Mathematical Finance, March 2015, Liquidation with Self-exciting Price Impact
  • Teaching

    I was Teaching Assistant responsible for the courses:

  • Mathematical Foundations for Finance, given by Prof. Teichmann, Winter semester 2014
  • Applied Stochastic Processes, given by Prof. Knowles, Spring Semester 2015
  • Probability and Statistics, given by Prof. van de Geer, Spring Semester 2017
  • I taught a weekly exercise class for the courses:

  • Mathematik I for Biology students, given by Dr. Caspar, Winter semester 2013 (in german)
  • Mathematical Foundation for Finance, given by Prof. Farkas, Winter Semester 2013
  • Wahrscheinlichkeit und Statistik for Electrical Engineering students, given by Prof. Nolin, Spring Semester 2014 (in german)
  • Mathematical Foundation for Finance, given by Prof. Schweizer, Winter Semester 2015
  • Wahrscheinlichkeit und Statistik for Computer Sciences students, given by Prof. Embrechts, Winter Semester 2015
  • Mathematik I for Biology students, given by Prof. Farkas, Winter semester 2016 (in german)
  • Curriculum

    Education

  • ETH/Zürich University, MSc in Quantitative Finance 2011-2013
  • ETH Zürich Master Applied Mathematics 2010-2012
  • Ecole Polytechnique Diplomé de l'Ecole Polytechnique 2007-2010
  • Languages

  • French: Native speaker
  • English: Full professional proficiency
  • German: Limited professional proficiency
  • Basic notions of: Chinese, Russian