A fractional Black-Scholes model with stochastic volatility and European option pricing

•European option pricing is studied under a FMLS model with stochastic volatility.•We have successfully solved a fractional partial differential equation system.•The derived pricing formula is truly explicit, involving no Fourier inversion. In this paper, we introduce the stochastic volatility into...

Full description

Saved in:
Bibliographic Details
Published in:Expert systems with applications 2021-09, Vol.178, p.114983, Article 114983
Main Authors: He, Xin-Jiang, Lin, Sha
Format: Article
Language:English
Subjects:
Cosine series
Exact solutions
Explicit and analytical
FMLS model
Fourier series
Fractional partial differential equation
Partial differential equations
Pricing
Securities prices
Stochastic models
Stochastic volatility
Volatility
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•European option pricing is studied under a FMLS model with stochastic volatility.•We have successfully solved a fractional partial differential equation system.•The derived pricing formula is truly explicit, involving no Fourier inversion. In this paper, we introduce the stochastic volatility into the FMLS (finite moment log-stable) model to capture the effect of both jumps and stochastic volatility. However, this additional stochastic source adds another degree of complexity in seeking for analytical formula when pricing European options, as the involved FPDE (fractional partial differential equation) system governing option prices is now of three dimensions. Albeit difficult, we have still managed to present an analytical solution expressed in terms of Fourier cosine series, after a two-step solution procedure is developed for the target FPDE system. This solution is different from the most literature as it is truly explicit, involving no Fourier inversion. It is also shown through the numerical experiments that it converges very rapidly and has potential to be applied in practice.
ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2021.114983