# The valuation of European option with transaction costs by mixed fractional Merton model

## TL;DR

This paper develops a discrete-time European call option pricing model using a mixed fractional Merton framework with transaction costs, highlighting the significant influence of time-step size and Hurst parameter on prices.

## Contribution

It introduces a novel mixed fractional Merton model for option pricing that incorporates transaction costs and analyzes the effects of key parameters.

## Key findings

- Time-step size significantly affects option prices.
- Hurst parameter impacts the valuation notably.
- Model properties are thoroughly explained.

## Abstract

This paper deals with the problem of discrete-time option pricing by the mixed fractional version of Merton model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. We also investigate the effect of the time-step $\delta t$ and the Hurst parameter $H$ on our pricing option model, which reveals that these parameters have high impact on option pricing. The properties of this model are also explained.