Finance, Risk, Asset-Pricing, Credit Scoring etc.


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An introduction to financial ideas for mathematicians; a basic course in financial mathematics covering

  • Risk-Neutral Asset Pricing
  • Financial Risk Theory
  • Finance, Risk and Uncertainty
  • Credit Scoring


(not final, may be changed slightly) 


Week 1 – Introduction to Mathematics in Finance  5/10 

Money. The significance of money to the development of mathematics. The ideas of arbitrage, interest and utility. 

Week 2 – Forward contracts, options, interest rates and swaps 12/10 

Introduction to the key derivative instruments. Model independent mathematical results. No arbitrage pricing of forward contracts and swaps. 

Week 3 – Single period derivative pricing and market incompleteness 19/10 

The fundamental intuition introducing the concept of risk-neutral pricing and the issue of market incompleteness. Introduction of the Radon-Nikodym derivative. Review of ideas in probability (sigma algebras, filtrations, stochastic processes, martingales) and their use in representing financial concepts (trading strategies). 

Week 4 – Multi-period discrete and continuous time models 26/10 

Discrete time derivative pricing leading to the Cox-Ross-Rubenstein model. Switching from discrete time to continuous time. Application of Ito’s Lemma and Cameron-Martin-Girsanov and Martingale Representation theories to arrive at the Black-Scholes-Merton Model. 

Week 5 – Consolidation/Assessment 2/11 

Week 6 – The Greeks and Volatility 9/11 

The relevance of ‘the Greeks’ to risk management. The issue of volatility and how it impact modern financial practice. Review of ‘Black Monday’ in October 1987, the Barings and LTCM failures. Discussion of the use of mathematical models in finance. 

Week 7 – Interest Rate Models 16/11 

Starting with Black’s Model and then moving on to Short Rate models, the Heath-Jarrow-Morton framework and introducing the Libor Market Models. 

Week 8 – Structured Finance and Securitisation Idea of securitisation 23/11 

Introduction of Credit Default Swaps and Asset Backed Securities. The Credit Crisis of 2008-2009. 

Week 9 – Risk Management 30/11 

Financial regulation environment including the distinctive nature of insurance. Introduction to the mathematical approaches. Credit risk modelling, both commercial (bonds) and retail (i.e. credit cards, personal loans). Introduction to the idea of liquidity risk and optimal trade execution. 

Week 10 – Numerical methods and assessment 7/12 

Overview of numerical approaches to derivative pricing and risk management. Introduction to ‘FinTech’.