Thesis supervisor: László Márkus
Location of studies (in Hungarian): "ELTE, TTK, Matematikai Intézet, Valószínűségelméleti és Statisztika Tanszék Eötvös Loránd University, Institute of Mathematics, Department of Probability Theory and Statistics" Abbreviation of location of studies: ELTE
Description of the research topic:
Asset price processes in continuous trading environment is often described by the exponential of Lévy processes, featuring jumps, or local or stochastic volatility models built on the basis of such processes. Naturally, the observed data available for these assets changes discretely in time. The character of the process and subsequently its parameters can only be identified on the basis of such observations. A wide range of researchers studied the problem for diffusion models given by stochastic differential equations, and a lot of results became available on the topic in this setup. However, for jump - specifically Lévy - processes the question is still subject of intense research, and despite of the available results it is far from being completely answered. The effective discretization with targeted choice of time points, drawing conclusion from the estimated parameters of the discretised model to the true parameters of the continuous model, the estimation of the error inherited from this procedure, the effective simulation, and the goodness of the simulated sample are all important subjects of study when a discretisation procedure is considered. An exciting option is to approximate the process with suitably chosen diffusion processes of continuous trajectory between relatively greater jumps, and apply or extend the results available for discretisation of diffusion processes to this case. Further, it is imperative to identify the character of the probability distribution of the process in question, and then estimate its parameters. The so called volatility, smile obtained from the option prices derived from the discretised model, is a frequently studied object. The calibration of the model to market prices on the basis of the smile is also a well-studied problem for diffusion models, and arises as an important question in the current setup as well.
Recommended language skills (in Hungarian): angol Number of students who can be accepted: 2