Pricing compound and extendible options under mixed fractional Brownian motion with jumps

TL;DR

This paper develops an analytical framework for pricing compound and extendible options where the underlying asset exhibits mixed fractional Brownian motion with jumps, providing formulas, special cases, and numerical insights.

Contribution

It introduces a novel analytical formula for compound options under mixed fractional Brownian motion with jumps, extending to extendible options and analyzing special cases.

Findings

Derived an explicit formula for compound options pricing.

Applied the formula to extendible options valuation.

Provided numerical results demonstrating the model's implications.

Abstract

This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these results are applied to value extendible options. Moreover, some special cases of the formula are discussed and numerical results are provided.