Quantitative Risk Management

MATH69551 Quantitative Risk Management 15 Semester 1 Postgraduate Taught Level 6 Sebastian Herrmann Unit coordinator Department of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 Everybody operating in the financial system needs to consider the possibility that they will make losses, whether this risk comes from changes in the value of their investments (an example of market risk), a borrower defaulting on a loan (credit risk), or unexpected natural disasters (operational risk). Furthermore, these risks come from many sources, and many of them are likely to be strongly linked. In this course, we look at how to quantify risk using probability theory. We will look at market risk and credit risk in detail, with an emphasis on the role that dependence plays in exacerbating or mitigating risk.   Everybody operating in the financial system needs to consider the possibility that they will make losses, whether this risk comes from changes in the value of their investments (an example of market risk), a borrower defaulting on a loan (credit risk), or unexpected natural disasters (operational risk). Furthermore, these risks come from many sources, and many of them are likely to be strongly linked. In this course, we look at how to quantify risk using probability theory. We will look at market risk and credit risk in detail, with an emphasis on the role that dependence plays in exacerbating or mitigating risk.   To provide a fundamental understanding of the mathematical approach to risk management in general, and market and credit risk in particular, with a focus on the modelling of dependencies in aggregate risk.   On completion of this unit, successful students will be able to: <ul> <li align="left"> Apply convex optimisation theory to solve unseen portfolio optimisation problems, and discuss the consequences of these solutions.</li> <li align="left"> Solve decision-making problems and interpret theoretical aspects and concrete situations in terms of risk aversion.</li> <li align="left"> Fit appropriate distributions to data, evaluate the fit and analyse the consequences.</li> <li align="left"> Evaluate risk from loss distributions using probabilistic and statistical tools.</li> <li align="left"> Model financial situations displaying dependence and interpret the results of this modelling.</li> <li align="left"> Develop and apply credit risk models.</li> </ul> <ul> <li> Portfolio management; convex optimisation</li> <li> Utility theory; risk aversion</li> <li> Risk measures; properties of risk measures</li> <li> Multivariate models for market risk: aggregate risk; loss distributions; normal and normal variance mixture distributions</li> <li> Extreme value theory</li> <li> Credit risk management: components of credit risk model; scoring and Merton models; mixture models; dependence between default events.  </li> </ul> 0 Other 20% 1 Written exam 80% Coursework- 20% (two pieces take home coursework, weight 10% each).Written exam at the end of the semester - 80% You will receive direct feedback on homework which you hand in, via marking of the work. Your marked coursework will include comments indicating where you performed well and where you could improve, which I hope you will be able to use in order to focus your revision. Please speak to me during tutorials, or come to my office hour, if you would like more personal feedback on your understanding or on a specific problem.   N McNeil, A., Frey, R. and Embrechts, P. Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton 2005.Ruppert, D. Statistics and Data Analysis for Financial Engineering.Springer, 2011.Ingersoll, Jonathan E. Theory of Financial Decision Making. Rowman & Littlefield, 1987. Lectures 26 Tutorials 12 0 112 This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates.