# 2008 Financial Crisis: Quantitative Analysis & Model Failures
> Explore the mathematical causes of the 2008 financial crisis, including Gaussian Copula failures, CDOs, leverage risks, and systemic economic impacts.

Tags: financial-crisis, quantitative-finance, systemic-risk, economics, housing-bubble, risk-management, statistics
## The 2008 Global Financial Crisis
* Perspective on systemic risk and model failure factors.

## Crisis Timeline & Propagation
* 2000–2006: Housing boom and credit expansion.
* 2008: Lehman Brothers collapse leading to global panic.
* 2009: Global recession.

## Housing Bubble: The Divergence
* Case-Shiller Index peaked around 185 in 2006 before crashing to 125 by 2010.

## Subprime Mortgages & Default Probability
* Issues: NINJA loans (no income verification), high LTV ratios, and Adjustable-Rate Mortgages (ARMs).

## The Illusion of Diversification: CDOs
* Tranches: Senior (lowest risk), Mezzanine, and Equity (highest risk).
* Reality: Systematic shocks affected all geographies simultaneously.

## The Culprit: Gaussian Copula
* Formula: P(joint default) = Φ_ρ ( Φ⁻¹(p₁), ... , Φ⁻¹(pₙ) ).
* Model fragility depends on ρ (Rho), the correlation parameter.

## Why the Model Failed
* Underestimated 'Fat Tail' risks.
* Based on limited historical growth data.
* Dynamics correlations trend toward 1.0 during crises.

## Leverage: The Magnifier
* Investment Banks reached 33x leverage in 2007.
* A 3.3% drop in assets wipes out 100% of equity at 30x leverage.

## Economic Impact: The Real Economy
* US Unemployment rate rose from 4.6% in 2007 to 9.6% in 2010.

## Lessons for Quantitative Finance
* Models are tools, not absolute truth.
* Stress testing must include 'impossible' scenarios.
* Quantitative methods should support human judgment.
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