Subdiffusive option price model with Inverse Gaussian subordinator
Volume 12, Issue 2 (2025), pp. 135–152
Pub. online: 12 November 2024
Type: Research Article
Open Access
Open Access
Received
16 January 2024
16 January 2024
Revised
6 August 2024
6 August 2024
Accepted
3 October 2024
3 October 2024
Published
12 November 2024
12 November 2024
Abstract
The paper focuses on the option price subdiffusive model under the unusual behavior of the market, when the price may not be changed for some time, which is a quite common situation in modern illiquid financial markets or during global crises. In the model, the risk-free bond motion and classical geometrical Brownian motion (GBM) are time-changed by an inverted inverse Gaussian($\mathit{IG}$) subordinator. We explore the correlation structure of the subdiffusive GBM stock returns process, discuss option pricing techniques based on the martingale option pricing method and the fractal Dupire equation, and demonstrate how it applies in the case of the $\mathit{IG}$ subordinator.
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