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

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 c...

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Bibliographic Details
Published in:Fractal and Fractional
Main Authors: Feng Xu, Xiao-Jun Yang
Format: Article
Language:English
Published: MDPI AG 2023-11-01
Subjects:
mixed weighted fractional Brownian motion
jump diffusion
European options
option pricing
fuzzy set theory
Online Access:https://www.mdpi.com/2504-3110/7/12/859
Description
Summary: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.
ISSN:2504-3110

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