Option Pricing Beyond Black-Scholes Based on Double-Fractional Diffusion

TL;DR

This paper introduces a double-fractional differential equation approach to option pricing, offering improved hedging against large price drops compared to traditional Black-Scholes-based options.

Contribution

It presents a novel double-fractional diffusion model for option pricing that enhances hedging effectiveness during market crashes.

Findings

Double-fractional model better captures market tail risks.

Options priced with the new model provide more reliable hedges.

Improved robustness of portfolios against dramatic price drops.

Abstract

We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the use of options whose prices were fixed by the Black-Scholes formula.