Αποτίμηση δικαιωμάτων μέσω της ανέλιξης Variance - Gamma

Στρατηγόπουλος, Χρήστος

Option pricing using Variance - Gamma process

Master Thesis

Author

Στρατηγόπουλος, Χρήστος

Date

2026-03

Abstract

The Black and Scholes model established the theoretical framework within which the systematic pricing of options became possible, with the corresponding formula serving as a benchmark in modern financial engineering practice. However, the well-known empirical inconsistencies of the model, such as the assumption of normality of logarithmic returns on securities and constant volatility, highlighted the need to incorporate additional complexity to model the underlying process. One approach to overcoming these limitations of the model involves studying models that introduce a jump component into price dynamics, such as those of pure-jump processes. Pure-jump processes are members of the class of Lévy processes, with the property that the paths are formed entirely via jumps, without the presence of a diffusion component. In this context, the Variance-Gamma process, as a typical example of the class of the processes mentioned above, emerges as a generalization of the classical Brownian motion diffusion model. Specifically, it is constructed by replacing the time index set of Brownian motion with a gamma process. This introduces the concept of "economic time", which reflects the idea that the rate of information evolution in markets is not determined by deterministic time intervals, but by stochastic mechanisms. This makes it possible to model different levels of volatility of the underlying security at different points in time of the economic time index, making the proposed model more suitable for adapting to the changing intensity with which information is passed on in the given market conditions. The model introduces two additional parameters that control the asymmetry and kurtosis of the return distribution, capturing more complex characteristics of the underlying security's dynamics. Valuation techniques based on both the analytical formula and the Esscher transformation were applied in order to calculate the value of the SPX derivative. The empirical results demonstrate that the proposed model achieves improved fit compared to the Black and Scholes model, which is a special case of the more general model developed in this MSc thesis.

Postgraduate Studies Programme

Εφαρμοσμένη Στατιστική

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

157

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/19138

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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Except where otherwise noted, this item's license is described as
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα