Record statistics and random walks in financial time series

Abstract

This project aimed at analysing the records statistics in stock price movements and mathematically model it. Probability distribution of the record gap for the stock price movements were determined. Power-law is observed in these probability distribution. Stochastic models namely, random walk without drift, random walk with finite drift and geometric random walk were simulated to generate time series which reproduces the signature properties of the stock price movements. These time series were then statistically analysed and probability distribution for record gaps was determined. Similar statistics were done for empirical stock market indices.