Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs

Abstract

This study investigates a new formula for option pricing with transaction costs in a discrete time setting. The value of the financial assets is based on time-changed mixed fractional Brownian motion [Formula: see text] model. The pricing method is obtained for European call option using the time-changed [Formula: see text] model in a discrete time setting. Particularly, the minimal value [Formula: see text] of an option respect to transaction costs is obtained. Furthermore, the new model for pricing currency option is presented by utilizing the time-changed [Formula: see text] model. In addition, the impact of time step [Formula: see text], Hurst parameter H and transaction costs [Formula: see text] are also investigated, which substantiate that these parameters play a significant role in our pricing formula. Finally, the empirical studies and the simulation findings corroborate the theoretical bases and indicate the time-changed [Formula: see text] is a satisfactory model.

Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps

“…ird, our model does not consider the constant periods of asset prices, which makes the application of the pricing model limited. Motivated by the aforementioned models in references [35][36][37][38][39][40][41] and the references therein, it is a good idea to construct a new pricing model for options under BFBM in subdiffusive regime.…”

“…en, the author obtained the fractional Fokker-Planck equation (in short, FFPE) governing the dynamics of the probability density function of the introduced process and the pricing formula for a European option in subdiffusive regime. is FFPE was first derived from the continuous-time random walks scheme with heavy-tailed waiting times (periods when the asset prices stay motionless) [36][37][38][39][40]. According to the distribution characteristics of waiting times, Magdziarz and Gajda [41] proposed a generalization of Black-Scholes model which was defined as standard GBM, subordinated by the infinitely divisible inverse subordinator.…”

The valuation of currency options by fractional Brownian motion

“…Typically, the Greeks are computed using a partial differentiation of the price formula Shokrollahi et al. ( 2015 , 2016 ).…”

Asset Pricing Model Based on Fractional Brownian Motion

“…Rao 2016 [20] priced the geometric Asian power option. Shokrollahi et al 2016 priced European options and currency options by time changed mixed fractional Brownian motion in [21]. Zhang et al 2020 proposed a fuzzy mixed fractional Brownian motion model with jumps in [22].…”