Financial modeling with Volterra Lévy processes and applications to options pricing, interest rates and credit risk modeling

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 models of interest rates, in particular the models of Vasicek, Cox-Ingersoll-Ross and Heath-Jarrow-Morton. Finally we study credit risk models
Document type :
Theses
Complete list of metadatas

Cited literature [101 references]  Display  Hide  Download

https://hal.univ-lorraine.fr/tel-01750699
Contributor : Thèses Ul <>
Submitted on : Thursday, March 29, 2018 - 12:52:51 PM
Last modification on : Thursday, September 27, 2018 - 3:48:50 PM

File

DDOC_T_2014_0042_EL_RAHOULI.pd...
Files produced by the author(s)

Identifiers

  • HAL Id : tel-01750699, version 1

Collections

Citation

Sami El Rahouli. Financial modeling with Volterra Lévy processes and applications to options pricing, interest rates and credit risk modeling. General Mathematics [math.GM]. Université de Lorraine, 2014. English. ⟨NNT : 2014LORR0042⟩. ⟨tel-01750699⟩

Share

Metrics

Record views

65

Files downloads

27