# Mathematical Finance

Module code: EC3081

Module co-ordinator: Dr Carlos Diaz Vela

Modern mathematical finance may be traced back to great papers by Markowitz (1959), Arrow (1964), Sharp (1964), Black and Scholes (1973), Merton (1973) and Cox, Ross and Rubinstein (1979). In this module you will study these developments with particular emphasis on their mathematical and statistical foundations and rigorous presentation.

Imagine that you are the Governor of the Bank of England. You are facing the prospect of an economic recession and you know well from your experience that what is needed is a cut in interest rate. But how much? The interest rate affects not only savings and investment, but also the exchange rate (which affects exports and imports), prices (especially house prices!), outputs and wages and much else beside. Each of these things affects the others in turn. Clearly you will need a mathematical model of the economy to trace all these interactions. But is the model correct? You will need to confront the model predictions with the evidence. This will need statistical methods, which themselves require maths.

In 2013 Mark Carney was appointed as Governor of the Bank of England, having previously held the same post at the Bank of Canada). To quote from Wikipedia "The epoch-making feature of his tenure as Governor remains the decision to cut the overnight rate by 50 basis points [0.5%] in March 2008. [This action] played a major role in helping Canada avoid the worst impacts of the financial crisis that began in 2007."

## Topics covered

• State preference theory
• Mean-variance theory
• Capital asset pricing model (CAPM)
• Arbitrage pricing theory (APT)
• An introduction to stochastic calculus
• Merton's model of the time evolution of prices of financial assets
• The Black-Scholes-Merton model for pricing financial derivatives

## Learning

• 20 one-hour lectures
• 10 one-hour tutorials
• 5 hours of project supervision

## Assessment

• Exam, 90 minutes (80%)
• Coursework (20%)