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Vrednotenje diskretnih azijskih opcij z Lévyjevimi procesi : magistrsko delo
Golob, David (Author), Košir, Tomaž (Mentor) More about this mentor... This link opens in a new window

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Abstract
V delu predstavimo metode za vrednotenje diskretnih azijskih opcij, ki temeljijo na Lévyjevih procesih. Metode bazirajo na izsledkih podanih v članku [10]. V modelih, ki jih uporabimo, je cena osnovnega sredstva modelirana z Lévyjevim procesom. V delu uporabimo različne Lévyjeve procese. Numerične metode, ki jih uporabimo so Monte Carlo simulacije in kvadraturna metoda za aritmetične opcije ter metoda Fourierjeve transformacije za geometrijske opcije. Za večjo natančnost Monte Carlo metod uporabimo kontrolno spremenljivko. Prav tako predstavimo metode za kalibracijo modela podatkom. V 2. poglavju opišemo glavne rezultate iz finančne matematike v zveznem času. V 3. poglavju opišemo Black-Scholes model ter njegove pomanjkljivosti. V 4. poglavju opišemo Lévyjeve procese. V tem poglavju predstavimo glavne lastnosti splošnih Lévyjevih procesov ter podrobne lastnosti za Lévyjeve procese, ki so uporabljeni v nadaljevanju tega dela. V 5. poglavju opišemo definicijo trga, kjer je vrednost osnovnega sredstva modelirana s Lévyjevim procesom. V tem poglavju je opisna tudi kalibracija modela. V 6. poglavju opišemo Monte Carlo metode ter metodo kontrolne spremenljivke. V 7. in 8. poglavju opišemo metode za vrednotenje diskretnih geometrijskih oziroma aritmetičnih azijskih opcij. V 9. poglavju so opisani rezultati kalibracije ter vrednotenja opcij. Zaključek je podan v 10. poglavju.

Language:Slovenian
Keywords:Azijske opcije, Lévyjevi procesi, Gaussova kvadraturna formula
Work type:Master's thesis/paper (mb22)
Tipology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2019
UDC:519.2
COBISS.SI-ID:18584921 This link opens in a new window
Views:721
Downloads:238
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Secondary language

Language:English
Title:Valuation of discrete Asian options with Lévy processes
Abstract:
In the thesis we describe methods for valuation of discrete Asian options based on Lévy processes. Methods described are based on article [10]. In models, which we use, the price of the underlying was modelled as exponential Lévy process. Applied numerical methods are Monte Carlo simulations, quadrature method for arithmetic Asian options and Fourier inversion method for geometric Asian options. For greater accuracy of MC simulations we use control variate. We also present method for calibration of the model to data. In Chapter 2 we describe main results of financial mathematics in continuous time. Black-Scholes model and its shortcomings are described in Chapter 3. Lévy processes and their properties are described in Chapter 4. In Chapter 5 Lévy market model is described together with the calibration of the model. Monte Carlo methods and control variate method are described in Chapter 6. In Chapters 7 and 8, valuation methods of discrete geometric and arithmetic Asian options are described. In Chapter 9 we describe results of model calibration and option valuation. The conclusion is given in Chapter 10.

Keywords:Asian options, Lévy processes, Gauss quadratu

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