Print Email Facebook Twitter Nonparametric Calibration of Inhomogeneous Lévy Processes using Fourier Techniques Title Nonparametric Calibration of Inhomogeneous Lévy Processes using Fourier Techniques Author Tendijck, Stan (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Söhl, Jakob (mentor) Jongbloed, Geurt (graduation committee) Meester, Ludolf (graduation committee) Degree granting institution Delft University of Technology Date 2018-09-04 Abstract In this report, inhomogeneous Lévy processes are studied in a discrete observational model based on derivatives of the process. First, homogeneous Lévy models are defined and an already known nonparametric method, using Fourier techniques and call and put option prices, for estimating the parameters of the model is described based on Belomestny and Reiẞ (2006a). Previous research suggests that there is a need for an extension of this concept since option prices with different maturities produce significantly different results. After all, the assumption that the parameters of the model are the same for any time window is not realistic and better results could be achieved once this premise is rejected. That is why inhomogeneous Lévy processes are introduced and studied in this report. The estimation method for the homogeneous model from Belomestny and Reiẞ (2006a) is extended to fit into the inhomogeneous framework. Next, asymptotic normality of the estimators is proven for these processes in this setting and confidence intervals are constructed using the finite sample variance method. Asymptotic normality has already been shown and confidence intervals have been constructed in the homogeneous framework in the continuous observational model by Söhl (2014). Finally, data is simulated from an inhomogeneous Merton model to test the performance of the method and options from the S&P 500 index are used as a real-world application. Subject StatisticsInhomogeneous Levy processesConfidence intervalsAsymptotic normality To reference this document use: http://resolver.tudelft.nl/uuid:6a8f5252-4842-4b47-bf41-cddc8ec6d83b Part of collection Student theses Document type master thesis Rights © 2018 Stan Tendijck Files PDF MasterThesisStanTendijck.pdf 1.19 MB Close viewer /islandora/object/uuid:6a8f5252-4842-4b47-bf41-cddc8ec6d83b/datastream/OBJ/view