Maximum likelihood estimation of stock volatility using jump-diffusion models

Abstract

We investigate whether there are systematic jumps in stock prices using the Brownian motion approach and Poisson processes to test diffusion and jump risk, respectively, on Johannesburg Stock Exchange and whether these jumps cause asset return volatility. Using stock market data from June 2002 to September 2016, we hypothesize that stocks with high positive (negative) slopes are more likely to have large positive (negative) jumps in the future. As such, we expect to observe salient properties of volatility on listed stocks. We also conjecture that it is valid to use maximum likelihood procedures in estimating jumps in stocks.

Keywords

• merton jump diffusion model
• black scholes volatility (iv) curves
• weiner process
• maximum likelihood estimation