Library:
Paris Champerret
Madrid
London
Paris Montparnasse
Turin
- Item type
- Study and report
- Dissertation
- Language
- English
- Publication year
- 2024
- Contributors
- KAHALE, Nabil
- Subjects
- FINANCES
This thesis explores the application of jump diffusion models in the context of financial modeling.
We begin by conducting a comprehensive research of three distinct diffusion models: The Merton
Jump Diffusion Model, the Kou Jump Diffusion Model, and the Extended Carr Madan Géman
Yor (CGMY) Model. Following this, we delve into Monte Carlo simulation techniques, emphasizing
simulation methods applicable to our models and variance reduction methods. Subsequently,
we optimize our models to match historical returns and real-market option prices, by implementing
and customizing Markov Chain Monte Carlo and Genetic algorithms. Finally, we validate our results
by comparison with the existing literature on the subject, specifically on calculated vanilla and exotic
option prices for known parameters.
