- This is a core module for the MSc in Mathematical Finance.
- Not available to undergraduate students.
- Lectures: 20 hours.
- Seminars/tutorials: 9 hours.
Financial Markets, Principles of Arbitrage and Valuation
- Modelling financial markets in one period Trading strategies and arbitrage opportunitiesStochastic discount factor and equivalent martingale measure. The fundamental theorem of asset pricing. Contingent claims, complete and incomplete markets
- Dynamic models in multiple periods Self-financing strategies. Valuation and hedging in complete markets. Sources of
incompleteness, approaches to valuation in incomplete markets
Modelling and Measuring Risk
- Different types of risk (operational, financial, market, credit, liquidity)
- Traditional approach and shortcomings
- Alternative approaches to modelling/measuring risk convex and coherent measuresValue-at-Risk (VaR), expected shortfall further measures
- Problems with empirical implementation
Decision-Marking under Uncertainty (Utility Theory)
- Traditional (von Neumann-Morgenstern) theory Lotteries and preference relations. Utility representation. Risk aversion and risk premium. Representative agents in complete markets
- Shortcomings of traditional theory and Alternatives Behavioural and cognitive biasesLoss aversion and prospect theory
Portfolio Allocation and Factor Models
- Single-Factor Models Mean-variance optimisation without a risk-free assetMean-variance optimisation with a risk-free asset. Tangency portfolio and capital markets line. Equilibrium and Capital Asset Pricing Model (CAPM)Tests and critiques of the CAPM
- General (Multi-)Factor Models General framework, factors and risk premiaSpecific examples (Fama-French, Carhart)Arbitrage-Pricing Theory (APT)
- Class Test 20%
- Group Project 20%
- Examination 1.5 hours 60%
Cochrane, J.H. (2001): “Asset Pricing” (2nd “revised” ed.) Princeton University Press
Campbell, J.Y. (2018): “Financial Decisions & Markets: A Course in Asset Pricing” Princeton University Press
Dumas, B. and E. Luciano (2017): “The Economics of Continuous-Time Finance” MIT Press
Föllmer, H. and A. Schied (2016): “Stochastic Finance” (4th ed.) Walter deGruyter, Berlin
McNeil, A., P. Embrechts, and R. Frey (2015): “Quantitative Risk Management” (2nd ed.) Cambridge University Press
Examination Period: January