Restrictions:

• This is a core module for the MSc in Mathematical Finance.
• Not available to undergraduate students.

Commitment:

• Lectures: 20 hours.
• Seminars/tutorials: 9 hours.

Content:

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)

Assessment:

• Class Test 20%
• Group Project 20%
• Examination 1.5 hours 60%

Illustrative Bibliography: