An Asymptotic Analysis of Risk in Financial Systems - Analysis and Algorithms

Anand Deo
Sandeep K Juneja
Wednesday, 25 Aug 2021, 18:30 to 19:30
Over the past few decades, probabilistic models have become an important tool for under-standing risks and decision making in practical financial systems. In the design of such systems one often wishes to relate the risk to the statistics of underlying stochasticity. However, this task is complicated by the fact that realistic financial systems are complex, and undesirable events in them are often rare. A large body of research has been devoted to understanding the nature of such rare events, and how they relate to the stochasticity affecting the system. In this talk, we undertake a detailed study of these aspects in order to develop structural insights on a number of financial systems of practical interest. Our main contributions are as below:
I. We discuss the development of a closed form, interpretable parameter estimation technique for predicting defaults of financial firms. Typically, one uses maximum likelihood estimation (MLE) for predicting the firm default probabilities. We prove that our estimator is almost as accurate as the MLE, verify our result empirically on a sample of US corporate data, and showcase the computational/interpretative benefits of our estimator over the MLE.
II. We develop a statistically consistent estimator for conditional value-at-risk (CVaR) based optimization objectives and their gradients. Unlike the state-of-the-art sample average approximations, the proposed approximation scheme exploits the self-similarity of heavy-tailed distributions to extrapolate data from lower quantiles, thereby reducing data requirements for accurate estimation.
III. Motivated by the increasing adoption of models which facilitate automation in risk management and decision-making, we present a novel importance sampling (IS) scheme for measuring distribution tails of objectives. Conventional efficient IS approaches suffer from feasibility concerns due to the need to intricately tailor the sampler to the underlying probability distribution and the objective. We overcome this challenge in the proposed black-box scheme by automating the selection of an effective IS distribution with a transformation that implicitly learns and replicates the concentration properties observed in less rare samples.
IV. We develop a limiting representation for an interconnected banking network in presence of partial information. Practical banking networks are large and complicated, and one searches for simple limiting representations (as the network size goes to infinity). We characterise the wealth of banks in a large network in terms of a simple, one dimensional distributional fixed point, which we show is amenable to Monte Carlo simulation.
This talk is based on joint work with Sandeep Juneja and Karthyek Murthy.

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