Subject: geometric Brownian motion; Fokker–Planck equation; Black–Scholes model; option pricing
Year: 2020
Type: Article
Title: [HTML] from mdpi.com Full View Generalised geometric Brownian motion: Theory and applications to option pricing
Author: Stojkoski, Viktor
Author: Sandev, Trifce
Author: Basnarkov, Lasko
Author: Kocarev, Ljupco
Author: Metzler, Ralf
Abstract: Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics, due to irregularities found when comparing its properties with empirical distributions. As a solution, we investigate a generalisation of GBM where the introduction of a memory kernel critically determines the behaviour of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and then obtain the corresponding probability density functions using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) in order to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness.
Publisher: MDPI
Relation: Entropy
Identifier: oai:repository.ukim.mk:20.500.12188/22954
Identifier: http://hdl.handle.net/20.500.12188/22954
