The Role of Mathematical Models in Financial and Health Crises
The 2007 Financial Crisis and Mathematical Models
In 2007, the total value of an exotic form of financial insurance known as Credit Default Swap (CDS) reached a staggering $67 trillion. This amount surpassed the global GDP by approximately fifteen percent. In simpler terms, a bet was made in the financial markets that exceeded the value of everything produced globally that year.
The bet was placed on whether Collateralized Debt Obligations (CDOs), a type of financial pyrotechnics, would explode. The insurance provider needed a high degree of certainty to place such a large bet.
The certainty was based on a formula known as the Gaussian Copula Model. This model estimated the joint probability that holders of any two randomly selected mortgages would both default. The model relied heavily on the gamma coefficient, which used historical data to estimate the correlation between mortgage default rates in different parts of the United States.
However, when real estate prices across the U.S. began to fall in the summer of 2006, many Americans decided to default on their mortgages. This led to a dramatic increase in the number of delinquent mortgages nationwide, causing the gamma coefficient in the Gaussian Copula Model to skyrocket. The result was a financial crisis in which the financiers who bet the entire planet's GDP lost.
The Covid-19 Pandemic and Mathematical Models
In the fall of 2019, a virus named SARS-CoV-2 began to spread from Wuhan, China. The world went into panic mode at the beginning of 2020, fearing that the infection fatality rate of the new virus would be comparable to its older siblings.
Academics around the world began to use mathematical models to make predictions about the virus's spread. However, these models were often overly simplistic, and the predictions they made did not match reality.
One of the most common models used was the SIR model, which stands for Susceptible–Infected–Recovered. This model treats people as colored balls that float in a container and bump into each other. However, the model does not account for geographical differences or multiple waves of contagion.
Despite the shortcomings of these models, they were used to justify various measures to combat the virus. These measures often had negative effects on people's mental and physical health.
The Climate Crisis and Mathematical Models
The consequences of mathematical models can also be seen in the discussion of climate change. This discussion can be divided into three parts: the real evolution of temperature on our planet, the hypothesis that an increase in CO2 concentration drives an increase in global temperature, and the rationality of the various measures proposed to prevent or mitigate climate change.
The hypothesis that an increase in CO2 concentration drives an increase in global temperature is supported by mathematical models. These models take into account a number of experimentally measured parameters, such as the spectrum of light absorption in CO2 and the temperature profile of the atmosphere.
However, the reliance on mathematical models raises concerns, especially in light of the failures of such models in the past. The "greenhouse effect" deserves more scrutiny, and it is important to have an open and honest professional debate on this topic.
Bottom Line
While mathematical models can be useful tools, they should not be relied upon unquestioningly. The financial crisis of 2007, the Covid-19 pandemic, and the ongoing climate crisis all demonstrate the potential pitfalls of relying too heavily on mathematical models. It's crucial that we approach these models with a healthy degree of skepticism and not mistake them for reality. What are your thoughts on the role of mathematical models in these crises? Share this article with your friends and sign up for the Daily Briefing, which is delivered every day at 6pm.
