Past Mathematical Finance Internal Seminar

9 June 2017
13:00
Pietro Siorpaes
Abstract


Martingale optimal transport is a variant of the classical optimal transport problem where a martingale constraint is imposed on the coupling. In a recent paper, Beiglböck, Nutz and Touzi show that in dimension one there is no duality gap and that the dual problem admits an optimizer. A key step towards this achievement is the characterization of the polar sets of the family of all martingale couplings. Here we aim to extend this characterization to arbitrary finite dimension through a deeper study of the convex order

 

  • Mathematical Finance Internal Seminar
19 May 2017
13:00
Abstract


I spent a number of years trading government bonds and interest-rate derivatives for Barclays Capital. This included the period of the financial crisis, and I was a colleague of some of the Barclays traders charged with fraud related to LIBOR rate manipulation. I will present a some examples of common trading scenarios, and some of the ethical issues these might raise for quants.
 

  • Mathematical Finance Internal Seminar
10 March 2017
13:00
Matthieu Mariapragassam and Andrei Cozma
Abstract

The efficient pricing and hedging of vanilla and exotic foreign exchange options requires an adequate model that takes into account both the local and the stochastic features of the volatility dynamics. In this joint work, we put forward a four-factor hybrid local-stochastic volatility (LSV) model that combines state-of-the-art dynamics for the exchange rate with stochastic dynamics for the domestic and foreign short rates, and provide a consistent and self-contained calibration and pricing framework.
For the calibration, we propose a novel and generic algorithm that builds on the particle method of Guyon and Labordere. We combine it with new variance reduction techniques to accelerate convergence and use control variates derived from a pure local volatility model, the stochastic short rates and the two-factor Heston-type LSV model. Our numerical experiments show a dramatic variance reduction that allows us to calibrate the four-factor model at almost no extra computational cost. The method can be applied to a large class of hybrid LSV models and is not restricted to our particular choice of the diffusion.
For the pricing, we propose a Monte Carlo simulation scheme that combines the full truncation Euler (FTE) scheme for the stochastic volatility and the stochastic short rates with the log-Euler scheme for the exchange rate. We find a lower bound on the explosion time of exponential moments of FTE approximations, and prove the strong convergence of the exchange rate approximations and the convergence of Monte Carlo estimators for a number of vanilla and exotic options. We then carry out numerical experiments to justify our choice of model and demonstrate convergence.
 

  • Mathematical Finance Internal Seminar
24 February 2017
13:00
Abstract


Speaker: Yixuan Wang
Titile: Minimum resting time with market orders
Abstract:  Regulators have been discussing possible rules to control high frequency trading and decrease market speed, and minimum resting time is one of them. We develop a simple mathematical model, and derive an asymptotic expression of the expected PnL, which is also the performance criteria that a market maker would like to maximize by choosing the optimal depth at which she posts the limit order. We investigate the comparative statistics of the optimal depth with each parameters, an in particular the comparative statistics show that the minimum resting time will decrease the market liquidity, forcing the market makers to post limit orders of volume 1.


Speaker: Marco Pangallo
Title: Does learning converge in generic games?
Abstract: In game theory, learning has often been proposed as a convincing method to achieve coordination on an equilibrium. But does learning converge, and to what? We start investigating the drivers of instability in the simplest possible non-trivial setting, that is generic 2-person, 2-strategy normal form games. In payoff matrices with a unique mixed strategy equilibrium the players may follow the best-reply cycle and fail to converge to the Nash Equilibrium (NE): we rather observe limit cycles or low-dimensional chaos. We then characterize the cyclic structure of games with many moves as a combinatorial problem: we quantify exactly how many best-reply configurations give rise to cycles or to NE, and show that acyclic (e.g. coordination, potential, supermodular) games become more and more rare as the number of moves increases (a fortiori if the payoffs are negatively correlated and with more than two players).  In most games the learning dynamics ends up in limit cycles or high-dimensional chaotic attractors, preventing the players to coordinate. Strategic interactions would then be governed by learning in an ever-changing environment, rather than by rational and fully-informed equilibrium thinking.
Collaborators: J. D. Farmer, T. Galla, T. Heinrich, J. Sanders

  • Mathematical Finance Internal Seminar

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