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http://hdl.handle.net/20.500.12188/22954
Наслов: | [HTML] from mdpi.com Full View Generalised geometric Brownian motion: Theory and applications to option pricing | Authors: | Stojkoski, Viktor Sandev, Trifce Basnarkov, Lasko Kocarev, Ljupco Metzler, Ralf |
Keywords: | geometric Brownian motion; Fokker–Planck equation; Black–Scholes model; option pricing | Issue Date: | 18-дек-2020 | Publisher: | MDPI | Journal: | Entropy | 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. | URI: | http://hdl.handle.net/20.500.12188/22954 |
Appears in Collections: | Faculty of Computer Science and Engineering: Journal Articles |
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