Programme Risk Day 2018

Abstracts

Mathieu Rosenbaum
No-arbitrage implies power-law market impact and rough volatility

Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that under no-arbitrage assumption, the market impact function can only be of power-law type. Furthermore, we prove that this implies that the macroscopic price is diffusive with rough volatility, with a one-to-one correspondence between the exponent of the impact function and the Hurst parameter of the volatility. Hence we simply explain the universal rough behavior of the volatility as a consequence of the no-arbitrage property. From a mathematical viewpoint, our study relies in particular on new results about hyper-rough stochastic Volterra equations.

This is joint work with Paul Jusselin.

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Til Schuermann
10 Years after Lehman: how has risk management changed?

The Lehman failure in September 2008 revealed the fragility of the global financial system. A lot has been done in the last decade to make that system more robust and less complex: improved market structures, more self-insurance through higher capital and more liquidity, somewhat credible resolution plans, and so on. Risk management has also changed, and I highlight three aspects: 1) use of stress testing; 2) more rigorous use of empirically grounded analytics and formal models; 3) model risk management. These three complementary changes have made both risk management more disciplined and more accessible to non-specialists that dominate senior management – and thus more influential.

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Darrell Duffie
No longer too big to fail

We estimate the impact of new regulations promoting the feasibility of administrative failure resolution of global systemically important banks (G-SIBs) on the cost of wholesale G-SIB debt financing. Based on a large panel data analysis and a model of the equity subsidy to G-SIBs associated with pre-crisis government bailouts, we show that G-SIBs with a given solvency buffer, adjusted for asset risk, have dramatically lower bailout probabilities and higher wholesale credit spreads in the post-crisis period relative to the pre-crisis period. In effect, G-SIB creditors now expect much larger losses in the event that a G-SIB approaches insolvency. In this sense, G-SIBs are "no longer too big to fail''.

This is joint work with Antje Berndt and Yichao Zhu.

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Isabelle Flückiger
AI in risk management and risk management in AI

Artificial intelligence, machine learning, deep learning, big data, cognitive systems, robotics and intelligent machines. The buzzword zoology has quickly grown over the last years, and the field is still developing rapidly, both in theory and practice. Risk management has become an important application area. On the other hand, concerns about the risks of artificial intelligence have arisen. I will share insights from my daily work in this emerging area illustrated by examples.

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Lukas Gonon
Hedging derivatives under market frictions using deep learning techniques

We consider the problem of optimally hedging a derivative in a scenario based discrete-time market with transaction costs. Risk-preferences are specified in terms of a convex risk-measure such as, for example, the Expected Shortfall. Such a framework has suffered from numerical intractability up until recently, but this has changed thanks to technological advances: using hedging strategies built from neural networks and machine learning optimization techniques, optimal hedging strategies can be approximated very well, as shown by the numerical study and the theoretical results presented in this talk.

This is joint work with Hans Bühler, Ben Wood and Josef Teichmann.

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Andrew Smith
Extreme value theory and American options

This presentation considers solutions for a class of optimal stopping problems, maximising the expected product of a Wiener process and a positive decreasing scale function. The general approach to such problems involves a partial differential equation (PDE) with movable boundary.
The method of images is a useful tool for solving fixed-boundary PDE problems. We adapt this method to a sub-class of movable boundary problems.
When the scale function in the original problem is a survival function of Generalised Pareto (GPD) type, we use a self-similarity property to reduce the PDE to an ODE. This ODE was widely studied in the 19th century, and the solution involves confluent hypergeometric functions. In cases of integer parameters, we give simpler closed form solutions involving the normal distribution function. The same approach also works when the Wiener process is reflected at zero.

This is joint work with Gabriela Baumgartner.

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Michael Studer
Private markets: challenges for risk managers

Private Markets as an asset class have significantly evolved over the last years. The size of the market has grown ten-fold since the nineties and investors continue to increase their allocations. Inherent challenges such as the absence of a widely accepted and established database like Bloomberg, the fact that there is no observable market price of assets and the illiquidity of the assets class pose significant challenges for risk managers.
We will detail some of the challenges and analyze a practical approach to measure and manage liquidity and market risk. Finally, we provide an outlook on areas for further research.

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