### Background Information

After the global financial crisis of 2007-2009, academics and corporations started to take interest in addressing risk that is inherent in the system, known as systemic risk. More specifically, systemic risk refers to the situation in which the failure of a bank or firm will cause the cascading failure of other firms in the system. As stated in “Systemic Risk and the Financial Crisis: A Primer”, the financial system had a significant source of risk from “default risk”, where a firm would not be able to live up to their obligations. This is a result of the interconnectedness, the leverage and the inclination for financial firms to finance long term assets with short term debt 2. Due to these three characteristics of financial firms if even one firm collapses, a multiple firm failure could occur. The failure of multiple firms at once, or in a short amount of time, is devastating to not only the financial market but also the global economy. Multiple firm failure almost occurred during the financial crisis, if not for the government stepping in and containing the failing banks. Before the financial crisis the systems in place to regulate and assess financial risk mostly looked at firms and markets in isolation 3. Thus there is now much more importance placed in modeling and understanding risk in general and systematic risk in particular. This problem has been approached in many ways in the last few years, including stochastic differential equations, graph theory, asymmetric coupling and how damage diversification can reduce systemic risk. In particular, our model will be a coupled stochastic differential equation based on the OU (Ornstein–Uhlenbeck) process which in the physical sciences can be used to describe processes such as integrate-and-fire neuron models, stress relaxation and dielectric relaxation time. In financial systems it is used by our model to describe the lending and borrowing between banks.

### Problem Statement

Systemic risk in financial systems is a major issue, and the factors that can result in systemic failure are still not fully understood. As established earlier, a systemic failure can have devastating consequences on the overall system. Thus we created a model, based on coupled stochastic differential equations (a Ornstein-Uhlenbeck process specifically), to simulate systemic risk in banking systems as to better understand some of the factors that influence systemic risk.

### Objectives of Project

The objectives of this project were to implement two existing models describing systemic risk, design and implement a third, understand the characteristics of the different models, and analyze how adjusting the parameters of the models affect the stability of the networks. The first model is an OU (Ornstein–Uhlenbeck) process, which simulates how banks lend and borrow with an adjustable level of interconnectedness. The second model improves upon the first model by incorporating graph theory to describe the connections between banks. After thoroughly understanding how the characteristics of the models influence the stability of the system, we improved upon the model.. The third model allows for different initial capital distributions and accounts for the difference in nominal capital between banks.