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Construction of a quantum finance model of option premia
Irinkov, Pavel ; Krištoufek, Ladislav (advisor) ; Avdulaj, Krenar (referee)
Last twenty years have seen a tremendous growth of the financial mar- kets both in trading volumes and in sophistication of instruments. This ever-increasing complexity of the market structure necessitates use of math- ematically advanced models from the side of market participants. So far, the prevalent paradigm for these models has been the stochastic analysis as a branch of applied mathematics. In the last few years however, there has been an influx of purely physical concepts and methodology, constituting nascent field of econophysics. To what extent this new approach is useful remains, however, an open question. In my bachelor thesis I will focus on one subfield of econophysics, namely quantum finance. First, I will give an overview of both stochastic analysis and the new quantum finance paradigm. Then using the framework of quantum theory and quantum field theory I will construct a model of European stock options. 1
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Pokles cen akcií v ex-dividend den a efektivnost trhů s akciovými opcemi
Křížek, Tomáš ; Dvořák, Petr (advisor) ; Stádník, Bohumil (referee) ; Svoboda, Martin (referee)
This paper analyses options/warrants price behavior around an ex-dividend day of underlying shares. Both equity options as financial instruments traded on options exchanges, and warrants/certificates as OTC financial instruments are analyzed. First, the paper analyzes the ex-dividend day share price drop. Findings of this part are further used to analyze the impact of unexpected share price decline on options prices. Further, the paper focuses on volumes of traded options contracts and changes in options prices around the ex-dividend day. The paper focuses on European shares and related options and warrants. The options data was collected from the options exchange EUREX and also from several OTC sources -- Vontobel, Lang & Schwarz, Erste, and xMarkets by Deutsche Börse. The main aim of the paper is to identify market inefficiencies in trading in and valuation of equity options. There are two main conclusions that around the ex-dividend day there is a significantly increased trading activity and the call options depreciate whereas put options appreciate between the cum-dividend and the ex-dividend day. This shows insufficient implementation of the share price drops into options valuation models of options dealers or investors / speculators. Further an impact of unexpected share price behavior was analyzed but no particular pattern has been identified. The impact of the unexpected share price drop (either too high or too low) has ambiguous implications on the options prices. Finally, ways how to utilize on knowledge of inefficient trading in options around the ex-dividend day were suggested. The suggestions were done both from the perspective of an investor / speculator and of an options dealer.
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