In recent years, there has been a fast growth in the application of long-memory processes to underlying assets including stock, volatility index, exchange rate, etc. The fractional Brownian motion is the most popular of the long-memory processes and was introduced by Kolmogorov in 1940 and later...

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...