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Hello, I have a question about network theory and systemic risk modeling. This question sort of rose to my mind after having written my thesis about systemic risk and contagion (spread of bankruptcies) in markets. I guess it's about the complexity of models, and how do you sort of control it / can they get too complex? Models based on network theory seem to resolve around Agent Based Modeling so maybe there is some insight someone can give to it? Alright, ill give some ground to this question.
Network theory models are mostly based around interbank network and their loans, but have gotten more complex in recent years to take in consideration second contagion channels, like overlapping portfolios of different entities (or nodes in the network). Nodes are most of the time balance sheets of banks, while edges are presented and loans between two banks.
At first, in 2000 Allen and Gale studied the interconnections between banks and the model was extremely simplistic, only had 4 banks and the loans between them were equal. They only wanted to see, that if banks had diversified between multiple partners, would the network be more resilient.
ALLEN, F., and D GALE (2000): “Financial Contagion,” Journal of Political Economy, 108(1), 1-33
In 2007, Nier et al. modeled the banking network on erdös-renyi random network, which means that banks made their loans randomly between themselves on certain p-value. Alright, obviously banks have some sort of incentives to make an loan to another bank, so its not completely random. But this model while simplistic, created multiple differently wired networks with different level of interconnection: It's enough to see, how contagion spreads and does stronger level of interconnection affect it. It also adds up to Allen and Gale, since network size is closer to real banking network size. Basically they ran multiple tests on different p-levels, took average from the amount of bankruptcies and tested if more interconnected network (high p-level) caused more or less bankruptcies. At this point it was pretty clear that most interbank networks in real life are core-periphery shaped, where there is certain banks in middle of network, highly interconnected. Periphery has most of the banks, and they mostly loan/borrow with the core banks. You could call those networks power law-based, but not quite. Erdös-renyi random networks are bell curve shaped.
Nier, E., Yang, J., Yorulmazer, T. & Alentorn, A. (2007). Network models and financial stability, Journal of Economic Dynamics and Control, Vol. 31(6), p. 2033-2060.
This tiering seen in real life interbank networks is next modeled by Krause and Giansante(2012), where they change the network shape by changing exponent in power law. They also try to make networks more realistic by randomizing the balance sheets of banks, although the balance sheets are still highly stylized. Basically contagion is still spread through interbank loans, but some banks might be less susceptible for contagion because of higher cash reserves. Basically the network is still created randomly, but nodes are created one by one and create their loan to other edges based on the amount of nodes other bank has. So its likely that network created has small core of banks, which are connected to large amount of banks with single edge. Well, intuitively in this network the bank wants to loan/borrow with banks that other banks want to loan/borrow with. Tests are ran with different power law exponent, higher exponent means that network is more interconnected/diversified while very high exponent has single bank in center loaning/borrowing with all banks in the system.
Krause, A. & Giansante, S. (2012). Interbank lending and the spread of bank failures: A network model of systemic risk, Journal of Economic Behavior and Organization, Vol. 83(3), p. 583-608.
All of the models stated above are static, meaning that banks don't change their loaning with others or try to get new capital from other banks. When contagion starts to spread, banks just sit there and either go bankrupt or not. Georg (2013) addresses this, and gives banks different incentives to loan and borrow. Some banks might have higher risk taking, investing in "risky" investments, which have high chance of negative returns but might also give large returns. Some banks might want to have higher liquidity, loaning from other banks. Some banks are risk averse, and don't want to loan to banks which have bad finance status. Basically the network formation is dynamic, and structure can change depending on the state of network.
Georg, C. (2013). The effect of the interbank network structure on contagion and common shocks, Journal of banking & finance, Vol.37 (7), p.2216-2228.
So next up is the multiplex networks, or "multiple layered" networks. These are used to represent different kind of connections. Think of them as networks which are on top of each other. For example loans can be different kind of loans, like overnight, short or long. Liu et al. (2020) takes this in to account in the ABM model. Another layer could be the owned assets between banks, or shares in other banks. For example Roykny et al. (2018) puts outside assets into the balance sheet (for example stocks), and some other bank can own a portion of those assets as well. For example banks are connected through a single stock, which price can fluctuate. If a bank goes bankrupt, fire sale can affect the price of stocks owned by other bank, leading to losses.
Roukny, T., Battiston, S. & Stiglitz, J.E. (2018). Interconnectedness as a source of uncertainty in systemic risk, Journal of Financial Stability, p. 93-106
Liu, A., Paddrik, M., Yang, S., Zhang, X. (2020). Interbank contagion: An agent-based model approach to endogenously formed networks, Journal of banking & finance, Vol.112, p.105-191
So now we step to the real which I myself don't quite understand. Basically the history in these models has been that they have been at first very stylished view on real world, trying to capture more and more dynamics of interbank networks. While capturing the dynamics, models have gotten harder and harder to intuitively understand, which at least in my view could eventually lead to dynamics in the modeled network, that doesn't really represent real world. How is the complexity controlled? or is it? I feel like this could lead to some sort of black box, which spits out an answer but there is no idea on how it lead to it, giving no real insight on how the contagion actually spreads/ how it can be controlled.
Also what is the industry view on ABM? Is systemic risk modeled this way? Or are these just seen in academia. I guess you could model a variety of interconnections between stocks / companies through this, atleast in theory.
Network theory models are mostly based around interbank network and their loans, but have gotten more complex in recent years to take in consideration second contagion channels, like overlapping portfolios of different entities (or nodes in the network). Nodes are most of the time balance sheets of banks, while edges are presented and loans between two banks.
At first, in 2000 Allen and Gale studied the interconnections between banks and the model was extremely simplistic, only had 4 banks and the loans between them were equal. They only wanted to see, that if banks had diversified between multiple partners, would the network be more resilient.
ALLEN, F., and D GALE (2000): “Financial Contagion,” Journal of Political Economy, 108(1), 1-33
In 2007, Nier et al. modeled the banking network on erdös-renyi random network, which means that banks made their loans randomly between themselves on certain p-value. Alright, obviously banks have some sort of incentives to make an loan to another bank, so its not completely random. But this model while simplistic, created multiple differently wired networks with different level of interconnection: It's enough to see, how contagion spreads and does stronger level of interconnection affect it. It also adds up to Allen and Gale, since network size is closer to real banking network size. Basically they ran multiple tests on different p-levels, took average from the amount of bankruptcies and tested if more interconnected network (high p-level) caused more or less bankruptcies. At this point it was pretty clear that most interbank networks in real life are core-periphery shaped, where there is certain banks in middle of network, highly interconnected. Periphery has most of the banks, and they mostly loan/borrow with the core banks. You could call those networks power law-based, but not quite. Erdös-renyi random networks are bell curve shaped.
Nier, E., Yang, J., Yorulmazer, T. & Alentorn, A. (2007). Network models and financial stability, Journal of Economic Dynamics and Control, Vol. 31(6), p. 2033-2060.
This tiering seen in real life interbank networks is next modeled by Krause and Giansante(2012), where they change the network shape by changing exponent in power law. They also try to make networks more realistic by randomizing the balance sheets of banks, although the balance sheets are still highly stylized. Basically contagion is still spread through interbank loans, but some banks might be less susceptible for contagion because of higher cash reserves. Basically the network is still created randomly, but nodes are created one by one and create their loan to other edges based on the amount of nodes other bank has. So its likely that network created has small core of banks, which are connected to large amount of banks with single edge. Well, intuitively in this network the bank wants to loan/borrow with banks that other banks want to loan/borrow with. Tests are ran with different power law exponent, higher exponent means that network is more interconnected/diversified while very high exponent has single bank in center loaning/borrowing with all banks in the system.
Krause, A. & Giansante, S. (2012). Interbank lending and the spread of bank failures: A network model of systemic risk, Journal of Economic Behavior and Organization, Vol. 83(3), p. 583-608.
All of the models stated above are static, meaning that banks don't change their loaning with others or try to get new capital from other banks. When contagion starts to spread, banks just sit there and either go bankrupt or not. Georg (2013) addresses this, and gives banks different incentives to loan and borrow. Some banks might have higher risk taking, investing in "risky" investments, which have high chance of negative returns but might also give large returns. Some banks might want to have higher liquidity, loaning from other banks. Some banks are risk averse, and don't want to loan to banks which have bad finance status. Basically the network formation is dynamic, and structure can change depending on the state of network.
Georg, C. (2013). The effect of the interbank network structure on contagion and common shocks, Journal of banking & finance, Vol.37 (7), p.2216-2228.
So next up is the multiplex networks, or "multiple layered" networks. These are used to represent different kind of connections. Think of them as networks which are on top of each other. For example loans can be different kind of loans, like overnight, short or long. Liu et al. (2020) takes this in to account in the ABM model. Another layer could be the owned assets between banks, or shares in other banks. For example Roykny et al. (2018) puts outside assets into the balance sheet (for example stocks), and some other bank can own a portion of those assets as well. For example banks are connected through a single stock, which price can fluctuate. If a bank goes bankrupt, fire sale can affect the price of stocks owned by other bank, leading to losses.
Roukny, T., Battiston, S. & Stiglitz, J.E. (2018). Interconnectedness as a source of uncertainty in systemic risk, Journal of Financial Stability, p. 93-106
Liu, A., Paddrik, M., Yang, S., Zhang, X. (2020). Interbank contagion: An agent-based model approach to endogenously formed networks, Journal of banking & finance, Vol.112, p.105-191
So now we step to the real which I myself don't quite understand. Basically the history in these models has been that they have been at first very stylished view on real world, trying to capture more and more dynamics of interbank networks. While capturing the dynamics, models have gotten harder and harder to intuitively understand, which at least in my view could eventually lead to dynamics in the modeled network, that doesn't really represent real world. How is the complexity controlled? or is it? I feel like this could lead to some sort of black box, which spits out an answer but there is no idea on how it lead to it, giving no real insight on how the contagion actually spreads/ how it can be controlled.
Also what is the industry view on ABM? Is systemic risk modeled this way? Or are these just seen in academia. I guess you could model a variety of interconnections between stocks / companies through this, atleast in theory.
