Past Mathematical Finance Internal Seminar

Today
13:00
Christoph Siebenbrunner and Andreas Sojmark
Abstract

Christoph Siebenbrunner:

Clearing Algorithms and Network Centrality

I show that the solution of a standard clearing model commonly used in contagion analyses for financial systems can be expressed as a specific form of a generalized Katz centrality measure under conditions that correspond to a system-wide shock. This result provides a formal explanation for earlier empirical results which showed that Katz-type centrality measures are closely related to contagiousness. It also allows assessing the assumptions that one is making when using such centrality measures as systemic risk indicators. I conclude that these assumptions should be considered too strong and that, from a theoretical perspective, clearing models should be given preference over centrality measures in systemic risk analyses.


Andreas Sojmark:

An SPDE Model for Systemic Risk with Default Contagion

In this talk, I will present a structural model for systemic risk, phrased as an interacting particle system for $N$ financial institutions, where each institution is removed upon default and this has a contagious effect on the rest of the system. Moreover, the financial instituions display herding behavior and they are exposed to correlated noise, which turns out to be an important driver of the contagion mechanism. Ultimately, the motivation is to provide a clearer connection between the insights from dynamic mean field models and the detailed study of contagion in the (mostly static) network-based literature. Mathematically, we prove a propagation of chaos type result for the large population limit, where the limiting object is characterized as the unique solution to a nonlinear SPDE on the positive half-line with Dirichlet boundary. This is based on joint work with Ben Hambly and I will also point out some interesting future directions, which are part of ongoing work with Sean Ledger.

  • 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

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