Completion, pricing and calibration in a Lévy market model

Download
index.pdf
2010
Yılmaz, Büşra Zeynep
Show full item record
187
views
107
downloads
In this thesis, modelling with Lévy processes is considered in three parts. In the first part, the general geometric Lévy market model is examined in detail. As such markets are generally incomplete, it is shown that the market can be completed by enlarging with a series of new artificial assets called “power-jump assets” based on the power-jump processes of the underlying Lévy process. The second part of the thesis presents two different methods for pricing European options: the martingale pricing approach and the Fourier-based characteristic formula method which is performed via fast Fourier transform (FFT). Performance comparison of the pricing methods led to the fact that the fast Fourier transform produces very small pricing errors so the results of both methods are nearly identical. Throughout the pricing section jump sizes are assumed to have a particular distribution. The third part contributes to the empirical applications of Lévy processes. In this part, the stochastic volatility extension of the jump diffusion model is considered and calibration on Standard&Poors (S&P) 500 options data is executed for the jump-diffusion model, stochastic volatility jump-diffusion model of Bates and the Black-Scholes model. The model parameters are estimated by using an optimization algorithm. Next, the effect of additional stochastic volatility extension on explaining the implied volatility smile phenomenon is investigated and it is found that both jumps and stochastic volatility are required. Moreover, the data fitting performances of three models are compared and it is shown that stochastic volatility jump-diffusion model gives relatively better results.
Lévy processes., Calibration., Pricing.
http://etd.lib.metu.edu.tr/upload/12612598/index.pdf
https://hdl.handle.net/11511/20156
Graduate School of Applied Mathematics, Thesis

Suggestions

Uncertainty quantification of parameters in local volatility model via frequentist, bayesian and stochastic galerkin methods
Animoku, Abdulwahab; Uğur, Ömür; Department of Financial Mathematics (2018)
In this thesis, we investigate and implement advanced methods to quantify uncertain parameter(s) in Dupire local volatility equation. The advanced methods investigated are Bayesian and stochastic Galerkin methods. These advanced techniques implore different ideas in estimating the unknown parameters in PDEs. The Bayesian approach assumes the parameter is a random variable to be sampled from its posterior distribution. The posterior distribution of the parameter is constructed via “Bayes theorem of inverse p...
Material Semiotics of Form Giving: The Case of the Electric Turkish Coffee Pot
Kaygan, Harun (MIT Press - Journals, 2016-03-01)
The article discusses material semiotics as a valuable framework for the analysis of design processes, and focuses on form giving practices. For this purpose, the design processes of electric Turkish coffee pots are studied through interviews and document analyses. It is argued that neither form giving nor product form can be considered to be singular or stable throughout a design process, and that semantic and material relations that are built and maintained around the product form need to be traced for a ...
Comparative analysis of variability modelling approaches in component models
Suloglu, Selma; Kaya, Muhammed Çağrı; Karamanlıoğlu, Alper; Entekhabi, Sina; Nikoo, Mahdi Saeedi; Tekinerdogan, Bedir; Doğru, Ali Hikmet (2018-12-01)
The results of a systematic literature review conducted for variability modelling in software component models are analysed and presented here. A well-planned protocol guided the screening of 3230 papers that resulted in the identification of 55 papers. Reviewing these papers, 23 of them were considered as primary studies related to our research questions. A comparison framework is introduced to further understand, assess, and compare those selected papers. Observations about the important aspects of compon...
Exploitation of multi-camera configurations for visual surveillance
Akman, Oytun; Alatan, Abdullah Aydın; Çiloğlu, Tolga (2008-06-20)
In this paper, we propose novel methods for background modeling, occlusion. handling and event recognition by using multi-camera configurations. Homography-related positions are utilized to construct a mixture of multivariate Gaussians to generate a background model for each pixel of the reference camera. Occlusion handling is achieved by generation of the top-view via trifocal tensors, as a result of matching over-segmented regions instead of pixels. The resulting graph is segmented into objects after dete...
Design of a magnetically tuned vibration absorber
Nakkaş, Halit Erdem; Özgen, Gökhan Osman; Department of Mechanical Engineering (2019)
In this thesis, a TVA is designed, manufactured and validated experimentally. The TVA uses eddy current effect as the damping mechanism with adjustable damping through changing distance between magnets and the conductors. In order to tune the damping level of the absorber to the desired range, magnetic analyzes are conducted and selection of conductor and magnets are made accordingly. Physical design of the TVA consists of a mass element, a spring element and a damping element. Compression helical spring is...
Citation Formats
B. Z. Yılmaz, “Completion, pricing and calibration in a Lévy market model,” M.S. - Master of Science, Middle East Technical University, 2010.
METU IIS - Integrated Information Service open@metu.edu.tr