Pricing Currency Option in a Mixed Fractional Brownian Motion with Jumps Environment

Abstract

A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a mixed fractional Brownian motion with jumps. The jump mixed fractional partial differential equation is obtained. Some Greeks and properties volatility are discussed. Finally the numerical simulations illustrate that our model is flexible and easy to implement.

Option Pricing for Processes Driven by Mixed Fractional Brownian Motion With Superimposed Jumps

“…After the original version of this paper was prepared, the author came to know of the work of Foad and Adem (2014) where similar results were obtained using slightly different techniques. They discuss pricing the currency option when the spot exchange rate follows the mixed fractional Brownian motion with the jumps following a Poisson process and jump size is log-normal.…”

Time-changed generalized mixed fractional Brownian motion and application to arithmetic average Asian option pricing

“…MFBM model has been employment for pricing currency option [16], pricing European options pricing Asian power options [2]. Especially in the emerging markets, the financial data represent the motionless periods, i.e.…”

Hedging in fractional Black–Scholes model with transaction costs

“…In the series of articles [11,13,14,15,16] the discrete hedging in the fractional Black-Scholes model was studied by using the economically dubious Wick-Itô-Skorohod interpretation of the self-financing condition. Actually, with the economically solid forward-type pathwise interpretation of the self-financing condition, these hedging strategies are valid, not for the geometric fractional Brownian motion, but for a geometric Gaussian process where the driving noise is a Gaussian martingale with the same variance function as the corresponding fractional Brownian motion would have, see [5,8,9,10].…”