James Shepherd of LSEG teaches this session of MIT's 18.642, Topics in Mathematics with Applications in Finance, on optimizing counterparty risk in derivative trading. He walks through the mathematical foundations of Value at Risk and Expected Shortfall as risk measures, then moves into the practical difficulties of margin calculation at financial institutions. The core of the lecture applies convex optimization techniques to minimize initial margin across networks of counterparties, with Shepherd working through the tradeoffs and fairness questions that arise when institutions share risk-reducing benefits unevenly. He grounds the theory in real-world implementation challenges that trading desks and clearinghouses actually face. Runtime is 81 minutes, consistent with the course's graduate-level treatment of quantitative finance topics, and the lecture assumes familiarity with probability and optimization fundamentals covered earlier in the series.