Learning Outcomes:
On completing this module students will
• be able to formulate a basic Financial Decisionmaking and/or Risk Management problem mathematically as a Constrained Optimisation problem and deploy a standard solver to obtain a solution
• Be able to compute (and simulate via Monte Carlo) Value at Risk, Expected Shortfall, and Credit Value Adjustment (CVA/XVA)
• know how to use derivative instruments to manage risk
• be able to use Latency and other Computational methods to detect heightened levels of Portfolio Risk (including Credit Risk)
• understand the principles and approaches to managing risk in a multi-period (dynamic) setting
Indicative Module Content:
In addition to a general overview of the qualitative issues encountered in Financial Risk management, the following
specific topics will be among those to be covered and emphasised.
-Optimal Long-term Investment Growth in a Multi-Period setting and the Information Theory ('Kelly') connection
-Mathematical Programming for Risk Management; Constrained optimisation (including Mean-Variance analysis)
-Arrow-Debreu Securities and Model-Free Derivatives Pricing
-Risk Assessment - Value at Risk (VaR) vs. C-VaR and other 'Coherent' risk measures, both parametric and Monte Carlo/Bootstrapping
-Methods for Credit/Debit Value Adjustment (CVA & DVA)
-Models for representing Statistical Association; Gaussian Copulae (plus associated pitfalls).
-General Multi-Period Financial Optimisation and Risk Management - Dynamic and Stochastic Programming
-Merton Model for Default
-Merton's Portfolio Problem (emphasis on definition, key results, and numerical approaches).
-Machine Learning models for Risk Management (Time Permitting)