Pricing European option with the short rate under Subdiffusive fractional Brownian motion regime

TL;DR

This paper develops a new option pricing model where the short rate follows a subdiffusive fractional Brownian motion, deriving explicit formulas and analyzing properties to improve accuracy in complex financial environments.

Contribution

It introduces an explicit pricing formula for European options under a subdiffusive fractional Brownian motion short rate model, extending the fractional Black-Scholes framework.

Findings

The model provides explicit call and put option formulas.

Numerical simulations show the model's flexibility and ease of implementation.

Properties of the model depend on parameters α and H.

Abstract

The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formula for call and put option and discuss the corresponding fractional Black-Scholes equation. We present some properties of this pricing model for the cases of $\alpha$ and $H$. Moreover, the numerical simulations illustrate that our model is flexible and easy to implement.