Pricing Compound and Extendible Options under Mixed Fractional Brownian Motion with Jumps

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.

Keywords

• pricing
• mixed fractional Brownian motion
• extendible and compound options
• poisson process