Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps

Abstract

The mixed fractional Brownian motion ( mf Bm ) has become quite popular in finance, since it allows one to model long-range dependence and selfsimilarity while remaining, for certain values of the Hurst parameter, arbitragefree. In the present paper, we propose approximate closed-form solutions for pricing arithmetic Asian options on an underlying described by the mf Bm . Specifically, we consider both arithmetic Asian options and arithmetic Asian power options, and we obtain analytical formulas for pricing them based on a convenient approximation of the strike price. Both the standard mf Bm and the mf Bm with Poisson log-normally distributed jumps are taken into account.

Call warrants pricing formula under mixed-fractional Brownian motion with Merton jump-diffusion

“…Additionally, [18,19] added jumps to the MFBM to value currency options, compound options, and extendible options. In [20], an actuarial technique was used to price Asian options under MFBM with jumps. On that account, and the similarities between options and warrants, [21] has investigated the pricing of warrants with the MFBM.…”