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## Andreea Minca, ORIE's Newest Faculty Member, Studies Contagion in Financial Networks

Bank A loans money to bank B, which loans to bank C (which may loan to A) and so on along a chain of transactions. What if somewhere along the chain one or more banks has inadequate capital to repay their loan, and defaults? What is the resulting risk to the other banks, and the risk of a cascade of defaults that impacts the banking system as a whole?

Assistant Professor Andreea Minca, who recently joined ORIE, has studied the resilience of financial networks to contagion and has proposed a framework for "stress testing" the extent of their resilience. Minca worked with Hamed Amini and Rama Cont to provide a precise theoretical underpinning to the intuitive notion that it is not necessarily those institutions with the largest balance sheets, but those that are most highly connected with and exposed to others that have the highest potential for creating instability in financial networks.

In principle, if the indebtedness to each other of all financial institutions in a network were known it would be possible to compute the impact on the network of a default of one or more loans in the system. But complete information about bilateral exposures is rarely available.

Computationally intensive simulation techniques can be used to understand resilience, but are too complicated and are not sufficiently flexible to adequately predict events in the future, according to Minca. Instead, her work "uses a simple analytical criterion for resilience to contagion, based on an asymptotic analysis of default cascades in heterogeneous networks." It does not require knowledge of the complete network and may be used to predict which institutions would pose the highest systemic risk under some well-defined stress test scenarios.

In April 2009, the U.S. Federal Reserve Bank's Supervisory Capital Assessment Program (SCAP) required comprehensive, consistent and simultaneous "stress testing" of the 19 bank holding firms with balance sheet assets exceeding $100 billion. However this testing did not explicitly consider the interconnected nature of these banks and of the financial network as a whole. "Their objective was to analyze systemic risk, but SCAP didn't really look at the system as a whole in order to do this" said Minca.

Diagrams such as this, of the Brazilian Interbank network, illustrate the complexity of banking networks. However data from which to construct such a diagram are not available for the U.S. system (source: Cont, Moussa and Santos). |

### Complementing stress tests

In their research, Minca and her coauthors have investigated the properties of random networks sharing essential characteristics with the real financial network. Through this work they have arrived at an empirical measure of resilience that complements the existing SCAP stress tests. "Our work shows that something akin to the 'law of large numbers' applies to large interbank networks," said Minca. (Similar modeling has been done by others investigating the spread of infectious diseases and the robustness of the Internet to targeted attacks).

The empirical resilience measure of Amini, Cont and Minca is such that it "may be implemented in a decentralized fashion by requesting banks to project the impact of a [given] macroeconomic stress scenario on their balance sheets." Each bank then assesses the number of institutions to whose default the bank would be vulnerable under the stress scenario, and reports it to the regulator. The empirical measure is a weighted sum of these numbers, subtracted from 1, where the weights depend on the connectivity. It summarizes the fact that "contagion is not only a matter of banks being too big to fail, but of being too interconnected and vulnerable to the default of immediate counterparties," Minca said.

In one simulation used to validate Minca's approach, two banks are selected at random from a sample network of 2000 institutions and are assumed to default. As the fraction of capital lost in a hypothetical stress scenario is increased, the number of consequent defaults remains small until the resilience measure goes negative, at which point the contagion cascades to the entire network. According to Minca, this graph is consistent with her theoretical results and shows the power of the resilience measure. "It is not a coincidence that the graphs cross right at the point of cascade," she said.

### An international scholar

Minca is originally from Bucharest, Romania, where she studied computer science at Polytechnique University of Bucharest before transferring to École Polytechnique on the outskirts of Paris. She received BS and MS degrees in applied mathematics there, and subsequently completed a postgraduate degree in probability and finance and a Ph.D. in applied mathematics at Pierre et Marie Curie University in Paris.

While pursuing her research, she did financial engineering work in industry. She contributed to construction of a platform for pricing financial derivatives called Premia (free for academic purposes) at INRIA, a worldwide information science and engineering organization based in France. In addition to Romanian and English, she speaks French and German.

"I'm very interested in applications of mathematics to finance, whether to derivatives, risk management or regulation," said Minca. "It is challenging to build mathematical models that are tractable and simple enough to understand but are sufficiently comprehensive," she said. "Nonetheless I believe operations research has more to contribute in these areas than many economists realize."

Minca enjoys hiking, biking, socializing with friends and watching films. At Ecole Polytechnique she participated in judo (which, like finance, entails leverage). She also did an internship in the technical department of the Bonn Opera in Germany and has performed in amateur theater.

### Credit default swaps

Minca and Cont are currently working on network models to assess systemic risk associated with an instrument known as a credit default swap (CDS). These transactions, which are a form of insurance, are the most relevant part of an over-the-counter derivatives market valued in the tens of trillions of dollars. As with interbank obligations, the CDS market is subject to cascades of contagion, which can be modeled using random networks. However in the CDS case, the network is more concentrated, since it contains dealer banks as well as other market participants. In a forthcoming paper, Minca and Cont explore resilience of such over-the-counter networks under stress, and show the valuable impact that a central clearing house (which has been proposed) would have on the size of an illliquidity cascade, provided that the clearing house is adequately capitalized.

Minca's work on applications in finance draws on nearly all of the areas involved with mathematical operations research: stochastic processes, statistics, optimization, simulation, information science, and network analysis. "It's great to have Andreea with us. Her work on stability and contagion in financial networks is exciting - both theoretically deep and highly topical," said ORIE Director Adrian Lewis. "Although she has been with us just a few weeks, she has already settled in as a key player in our financial engineering enterprise."