Paul Glasserman (Columbia University)

Title “Bounding Wrong-Way Risk in CVA Calculation”

Abstract: Counterparty risk depends on the interaction between market and credit risk. Positive dependence between the two creates “wrong-way risk”, the risk that a counterparty is more likely to default when the exposure to the counterparty is greater. This is reflected in a higher value for the credit valuation adjustment, or CVA. The dependence between market and credit risk is difficult to model, so we develop methods for bounding it by finding the worst-case joint distribution given constraints on the marginal models of market and credit risk. The methods work with simulated paths of market exposure and simulated or implied default-time distributions. A tractable optimization problem finds the worst-case joint distribution based on a finite number of paths; we show that the in-sample worst-case CVA converges to the theoretical worst case as the number of paths grows. We also develop a method to “interpolate” between the worst case and the independent case, based on the degree of uncertainty in the dependence, by penalizing deviations from a reference model. Here too we establish consistency of the resulting estimator. This is joint work with Linan Yang.

Matheus Grasselli (Fields Institute Toronto)

Title : “Macroeconomics – the final frontier for mathematical finance”

Abstract: Still grappling with the aftermath of the Great Depression, macroeconomics was a hotbed for mathematical modeling from the 1940s to the 1970s. As the memories of the depression faded and the ideological pendulum swung back towards free market fundamentalism, a reductionist search for so-called microfoundations turned the discipline into a branch of optimization and equilibrium. Accordingly, the role of banking and finance in these microfounded macroeconomic models was reduced to passive intermediation designed to address frictions in an otherwise perfect matching of lenders and borrowers. It took another crisis of global proportions to shake this view. In this talk, I shall present models where banking and finance play a much more fundamental role in economic activity. In particular, I’ll analyze the Great Moderation, the crisis of 2008, the slow recovery that followed, and the topical notion of ‘secular stagnation’ through the lenses of mathematical models for expansion and contraction of private debt.

David Hobson (University of Warwick)

Title : “Gambling in contests”

Abstract: (Joint work with Han Feng). In a recent paper in the Journal of Economic Theory Seel and Strack introduced a gambling contest. Each agent observes and independent copy of a diffusion and chooses when to stop it (based solely on the information from their own process). The winner of the contest is the agent whose stopped process has the highest value. In this talk we rederive the form of the optimal strategy for the agents, and discuss several extensions.

Andrei Kirilenko (Massachusetts Institute of Technology)

Title : “High Frequency Trading”

Abstract: High frequency trading is a recent innovation in financial intermediation that does not fit neatly into a standard liquidity-provision framework. While the net contribution of high frequency trading to market dynamics is still not fully understood, their mere presence has already shaken the confidence of traditional market participants in the stability and fairness of the financial market system as a whole.

Georges Papanicolaou (Stanford University)

Title : “Systemic risk”

Abstract: The quantification and management of risk in financial markets is at the center of modern financial mathematics. But until recently, risk assessment models did not consider seriously the effects of inter-connectedness of financial agents and the way risk diversification impacts the stability of markets. I will give an introduction to these problems and discuss the implications of some mathematical models for dealing with them.

Mete Soner (ETH Zurich)

Title : “Quasi sure analysis, 2BSDE’s and duality”

Abstract: Stochastic analysis under a class of measures has many applications. In finance, it provides a mathematical approach for model uncertainty. In backward stochastic differential equations it allows one to obtain representations for fully nonlinear parabolic equations. In this talk, I will survey these connections, and the new duality results in this more general setting. Also, I will also discuss the implications of these duality results on the fundamental theorem of asset pricing.

Peter Tankov (Paris Denis Diderot University)

Title : “Tail asymptotics of log-normal portfolios”

Abstract: (Joint work with Archil Gulisashvili)

In this talk, we present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior turns out to be determined by a subset of components of the Gaussian vector, and we identify the relevant components by relating the asymptotics to a tractable quadratic optimization problem. As a corollary, we characterize the limiting behavior of the conditional law of the Gaussian vector, given a linear combination of the exponentials of its components. Contrary to earlier works on small-noise asymptotics, which sometimes require solving a non-convex optimization problem [1], our approach leads to fully explicit results. These results have a wide range of applications in risk analysis of log-normal portfolios. Among other issues, we shall discuss

• Explicit variance reduction methods for precise estimation of tail event probabilities by Monte Carlo.

• Behavior of long only and long-short portfolios in the multidimensional Black-Scholes model under market downturns and systematic design of stress tests for such portfolios.

Extensions to distributions and dependence structures other than multivariate log-normal will also be mentioned.

References

[1] Avellaneda, M., Boyer-Olson, D., Busca, J., and Friz, P., Reconstructing volatility: Pricing index options using the steepest-descent approximation, Risk 15 (10), 87-92 (2002).

[2] Gulisashvili, A. and P. Tankov, Tail behavior of sums and differences of log-normal random variables, Arxiv preprint 1309.3057 (2013).

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