18.642 | Fall 2024 | Undergraduate

Topics in Mathematics with Applications in Finance

Week 6

Lecture 10

Guest lecture with James Shepherd, Quantile Technologies (LSEG)

Video description: This lecture by James Shepherd from LSEG provides an in-depth explanation of counterparty risk optimization in derivative trading, focusing on key risk measures like Value at Risk (VaR) and Expected Shortfall. It covers the mathematical foundations, practical challenges in margin calculation, and the use of convex optimization techniques to minimize initial margin across networks of financial institutions, highlighting the complexities of real-world implementation and fairness considerations.

Counterparty Risk Optimization Slides (PDF)

Lecture 11

Video description: This lecture covers the theory and application of regression modeling, including linear regression properties, hypothesis testing, and advanced methods like ridge, lasso, and principal components regression. It also explores practical use cases such as ETF sector regressions and empirical analysis of the Capital Asset Pricing Model, highlighting model diagnostics, parameter estimation, and challenges like residual distribution and regime changes.

Regression Analysis Slides (PDF)

Regression Analysis Notes (PDF)

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Fall 2024
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