Reference : Financial modeling with Volterra Lévy processes and applications to option pricing, i...
Dissertations and theses : Doctoral thesis
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/16617
Financial modeling with Volterra Lévy processes and applications to option pricing, interest rates and credit risk modeling
English
Elrahouli, Sami Abdul Latif mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
28-Feb-2014
University of Luxembourg, ​Luxembourg, ​​Luxembourg
Docteur en Mathématiques
133
[en] Fractional Brownian motion ; Fractional Black Scholes ; credit risk ; Lévy processes ; Arbitrage ; intrest rate
[en] Abstract. This work investigates financial models for option pricing, interest rates and credit risk with stochastic processes that have memory and discontinuities. These models are formulated in terms of the fractional Brownian motion, the fractional or filtered Lévy process (also doubly stochastic) and their approximations by semimartingales. Their stochastic calculus is treated in the sense of Malliavin and Itô formulas are derived. We characterize the risk-neutral probability measures in terms of these processes for options pricing models of Black-Scholes type with jumps. We also study interest rates models, in particular the models of Vasicek, Cox-Ingersoll-Ross and Heath-Jarrow-Morton. Finally we study credit risk models.
Researchers ; Students
http://hdl.handle.net/10993/16617

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