Estimation of bid and ask pricing for European option under mixed fractional Brownian motion environment with superimposed jumps

TL;DR

This paper develops a model for estimating bid and ask prices of European options considering a mixed fractional Brownian motion with jumps, providing a more accurate reflection of market dynamics.

Contribution

It introduces a novel approach combining mixed fractional Brownian motion and jump processes for option pricing, enhancing existing models.

Findings

Derived explicit formulas for bid and ask prices.

Demonstrated the impact of jumps on option valuation.

Validated the model with numerical simulations.

Abstract

We investigate the valuation of the bid and ask prices for European option under the mixed fractional Brownian motion environment in the presence of superimposed jumps by an independent Poisson process.