A fractional version of the Merton model.
In this paper, the impact of long-range dependence on the option pricing is investigated. The authors consider the option pricing problem while the dynamics of stock log-price follow a fractional jump-diffusion process with Hurst exponent \(H>1/2\). So, the sample paths of log-prices of the stocks exhibit long-range dependence and look as if they are fractional Brownian motions, although occasional jumps will be noticeable. The price of a European call option is derived. It does not contain explicitly the volatility, therefore the call premiums are ``smaller'' than those of the Merton's call. Finally, the relation between Hurst exponent and long-range dependence is discussed.
scientific article; zbMATH DE number 2027019