Main Topics and Lecturers:
Channels of contagion in financial systems
Rama Cont (Imperial College London)
Understanding the mechanisms underlying systemic risk requires to shift from the traditional focus on single-portfolio risk modeling and examine the link between the structure of the financial system and its stability, with a focus on contagion mechanisms which may lead to large scale instabilities in the financial system. Some channels of contagion which have played an important role in past crises are: insolvency contagion through counterparty exposures, withdrawal of liquidity in funding channels and price-mediated contagion [4,5,8] through fire salesof assets.
The course is a review of some recent work on the mechanisms underlying these channels of contagion, with a focus on the nature and granularity of the ‘network’ underlying each contagion mechanism and the implications of these results for the monitoring and regulation of systemic risk.
Resilience to contagion in financial networks
Network structure and systemic risk in banking
Stress testing the resilience of financial networks
- H Amini, R Cont, A Minca (2016) Resilience to contagion in financial networks. Mathematical Finance. Volume 26, Issue 2, April 2016, p 329–365.
- H Amini, R Cont, A Minca (2012) Stress testing the resilience of financial networks, International Journal of Theoretical and applied finance, Vol 15, 1250006.
- R Cont, A Moussa, E B Santos (2013) Network structure and systemic risk in banking systems in: J.P. Fouque & J. Langsam (Eds.) Handbook of Systemic Risk, Cambridge University Press.
- R Cont, L Wagalath (2013) Running for the exit: short selling and endogenous correlation in financial markets. Mathematical Finance, Vol 23, Issue 4, p. 718-741, October 2013.
- R Cont, L Wagalath (2016) Fire sale forensics: measuring endogenous risk. Mathematical Finance. Vol 6, No. 4, 835-866.
- R Cont, Th Kokholm (2014) Central Clearing of OTC Derivatives: bilateral vs multilateral netting, Statistics and Risk Modeling, Vol 31, No 1, 3-22.
- R Cont, A Minca (2016) Credit default swaps and systemic risk, Annals Of Operations Research. Vol 247, 523–547.
- R Cont, E Schaanning (2015) Fire sales, indirect contagion and systemic stress-testing, http://ssrn.com/abstract=2541114
Cascade models in large financial networks
Tom Hurd (McMaster University)
This minicourse aims to provide a unified mathematical framework for the primary channels that can transmit damaging shocks through financial systems. It will explore extensions of the material contained in my book, “Contagion! Systemic Risk in Financial Networks”. It is intended for quantitative finance practitioners, financial regulators and a broad range of academics including economists, physicists, applied mathematicians and computer scientists.
Outline of topics:
- Cascade Mechanisms and Cascade Equilibrium: extending the Eisenberg-Noe 2001 framework to other contagion mechanisms, including Gai-Kapadia 2010 and the Asset Fire Sale Model.
- Random Graph constructions: Assortative configuration graphs, scale-free preferential attachment graphs and inhomogeneous random graphs.
- Finance Cascade analytics: Random Financial Networks, the Without Regarding condition, locally tree-like independence, Cascade Mapping Theorems.
Clearing in financial systems
Yuri Kabanov (Université Bourgogne Franche-Comté)
- The Eisenberg-Noe-Suzuki model. Existence of the clearing vectors via fixpoint theorems. Uniqueness theorem.
- The Rogers-Veraart model. Calculation of the largest clearing vector.
- The Suzuki-Elsinger model with crossholdings.
- The Elsinger model with seniorities of liabilities.
- The Fisher model with CDS.
- Models with illiquid securities.
Modeling systemic risk
Andreea Minca (Cornell University)
This short series of lectures will present the state of the art in modeling systemic risk. We will be discussing cascade models in inhomogeneous random financial networks, which are amenable to data.
Next, we will discuss a novel framework for the control on interbank contagion. Particular emphasis is placed on core-periphery networks, and on strategies of risk mitigation in such networks. A new type of stochastic control is discussed, when uncertainty is about network structure. The control is adapted to a link-revealing filtration, which models the spatial progression of contagion.
Last, time permitting, we will develop models that are rooted into insurance mathematics, so that we provide answers to questions pertaining to central clearing.
The outline is as follows:
- Inhomogeneous random graphs and large cascade tests.
- Control of interbank contagion under partial and complete information.
- Central clearing model using star networks with Sparre-Andersen processes representing the nodes' capital; Fair membership strategies.
Book of abstracts of the winter school