Pricing European Options under a Fuzzy Mixed Weighted Fractional Brownian Motion Model with Jumps

Abstract

This study investigates the pricing formula for European options when the underlying asset follows a fuzzy mixed weighted fractional Brownian motion within a jump environment. We construct a pricing model for European options driven by fuzzy mixed weighted fractional Brownian motion with jumps. By converting the partial differential equation (PDE) into a Cauchy problem, we derive explicit solutions for both European call options and European put options. The figures and tables demonstrating the effectiveness of the results highlight the suitability of the fuzzy mixed weighted fractional Brownian motion with jump model for option pricing.

Keywords

• mixed weighted fractional Brownian motion
• jump diffusion
• European options
• option pricing
• fuzzy set theory