At the start of the financial crisis of 2008, the investment bank Lehman Brothers defaulted and went bankrupt. Within days, American International Group Inc. (AIG), a huge multinational insurance company, looked as if it, too, would go under. The failures of Lehman and AIG were connected because they were entangled in a financial network of credit default swap (CDS) contracts. These are insurance contracts against corporate default. When Lehman fell, AIG was required to make good on over $400 billion in CDS contracts it had with Lehman. AIG had nowhere near the capital to pay out that much.
This chain of events shows the dangers of interconnection in financial networks, says Andreea C. Minca, Operations Research and Information Engineering. “There are a variety of ways firms and banks are connected,” she says. “Financial derivatives such as credit default swaps are one way. Loans are another. And there are indirect channels as well. For instance, firms can hold the same portfolios, and if one of them is in distress and sells some of those assets, that is going to have an impact on the assets’ prices, which will affect everyone who holds them.” The impact could spread far, ultimately affecting a range of investors from pension funds and retail investors to university endowments.
A Formula for Quantifying Risks in Financial Networks
It’s important to understand the risk inherent in financial networks according to Minca, whose research focuses on mathematical modeling in finance within the areas of systemic risk, liquidity risk, and credit risk. She has been modeling connections between financial institutions as a way to quantify financial stability and to look for contagious linkages—potentially dangerous connections where the distress of one institution will threaten its neighbors.
“You need very advanced mathematical tools to quantify risk in such complex systems,” she explains. “I’m using proof theorems to find how far a contagion goes in a financial network.” Minca is also looking to define the characteristics of the institutions in the network in an effort to prevent contagion. If there is a concentration of dangerous links in key nodes within the network—exposures that are so large the capital or liquidity of the firm cannot withstand them—she suggests an increase of capital or liquidity at those banks.
“We find indicators of financial instability,” she says. To do this she uses a formula with multiple inputs, such as the fraction of banks in the network with large connectivity to other members, the fraction that have medium connectivity, and the fraction of contagious linkages. “The formula will tell you, if a certain quantity is higher than one, with high probability, the network is prone to contagious risk,” she says. “This means that the default of one or two institutions could affect a large fraction of the network.”
“Firms can hold the same portfolios, and if one of them is in distress and sells some of those assets, that is going to have an impact on the assets’ prices, which will affect everyone who holds them.”
The Bank Stress Test
The situation with AIG and Lehman Brothers in 2008 is an example of what Minca is looking for. “AIG was a key node in that network,” she says. “If we could have looked at the data and the exposures of AIG back then, looked at that high concentration of derivatives, I’m pretty sure those were contagious links.”
Minca’s research findings have been integrated into bank stress tests, designed to ascertain whether a bank has the capital to withstand various adverse developments. In the United States, banks with $50 billion or more in assets are required to conduct annual federal stress tests as well as semi-annual company-run stress tests. “Banks that fail a stress test today have to raise new capital,” Minca says.
A Mathematical Game for Early Warning Signs of Bankruptcy
In another project, Minca and her collaborators are looking at game theoretic models for bank runs. “Our idea is that if we think about investors being strategic and if we are able to describe their decision-making process using a mathematical model, then looking at the data, we can also derive early warning signals for bankruptcy,” Minca says. To predict when a bank run might happen, the researchers establish a mathematical game between all the various financers of the bank. The goal is to find the Nash equilibrium of the game, the point at which each lender knows the other lenders’ equilibrium strategies, and each has no incentive to deviate from their equilibrium choice given that the others keep to their choices.
“We created a model that has as one if its key ingredients the belief of the lenders about the prospects of the borrower,” Minca says. “Then we defined the mathematical game in which they have several choices: either to keep on investing or to withdraw.” Using their model, Minca and her collaborators derive the fraction of investors that will keep investing in the firm and identify when that fraction is insufficient for the firm to be able to refinance itself.
Clearinghouses for a Transparent, Safer Derivatives Market
In December 2016, Minca was awarded a National Science Foundation Faculty Early Career Development award for $500,000 over five years. She intends to use the funding to research the optimal guidelines for central clearinghouses tied to the derivatives market, which were mandated as part of the Dodd-Frank Act enacted by the United States Congress in 2010. To make the derivatives market more transparent and safer, central clearinghouses act as the intermediary between any two principles of a contract. Their purpose is to guarantee there is no default on the contract.
“The clearinghouse is supposed to have adequate layers of protection, adequate layers of capital such that it is virtually risk free,” Minca says. “But how do you do this in practice? The capital is supposed to come from the members of the clearinghouse. We are asking, ‘What are the fair contributions of these members? And how are we going to do an optimal design of the rules around the clearinghouse itself?’”
Minca finds financial markets fascinating because of the complexity of the problems and the tools needed to solve them. “The network is a top-down view; you see it from afar,” she says. “When you look at the problem with borrowers and lenders, you’re looking closer at the microstructure of the funding market. Then the clearinghouses are another point of view. You have to make sense of these different snapshots at different distances from the firms and the financial systems. It’s like a puzzle.”
She was especially pulled to apply her expertise to that puzzle after the 2008 financial upheaval. “There were so many questions left unanswered after the crisis,” she says. “The urgency of it was striking to me. So much of the economy was affected. We don’t want another crisis like that. There has been great momentum to change how the financial landscape looks. I want to be a part of that.”