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...

In modelling financial derivatives, the pricing of barrier options are complicated as a result of their path-dependency and discontinuous payoffs. In the case of rebate knock-out barrier options, discount factors known as rebates are introduced, which are payable to the option holder when the...