The standard mathematical model of random asset price variation is Geometric Brownian Motion – where the log of the asset price ‘return’ is normally distributed. However, this under-predicts the frequency of dramatic and large changes in the price. In real data, ‘fat-tails’ are observed, meaning that large deviations from mean behaviour are seen more often than in GBM – see here or here . A multifractal approach promises more realistic behaviour. This project would investigate possible uses of multifractal models in finance.
Supervisor: Dr David Graham