Integrals, Jump-Diffusion Processes and Monte Carlo Simulation
Public Deposited- Resource Type
- Creator
- Abstract
This master thesis is to fulfill the curiosity in how special characteristics of Brownian motion motivate the development of Ito calculus from Stieltjes integral. We will see the general Stieltjes integral theories and how the concept of p-variation plays a determining role and the case where the fractional Brownian motion can also be an integrator under the Stieltjes scope. Then we will give a tour of the distinctive traits of Brownian motion and how they mark the necessity to evolve a new Ito integral. Subsequently, we expand the integrator in Ito integral to jump-diffusion processes. Thereafter, we see how these new stochastic processes play a role in modelling financial assets and how sample paths of these stochastic processes can be generated using simulation and examplify the fact that Jump-Diffusion models are improvements from classical Black-Scholes-Merton model to incorporate the fat tail effects exhibited in empricial financial data.
- Subject
- Language
- Publisher
- Thesis Degree Level
- Thesis Degree Name
- Thesis Degree Discipline
- Identifier
- Rights Notes
Copyright © 2014 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
- Date Created
- 2014
Relations
- In Collection:
Items
Thumbnail | Title | Date Uploaded | Visibility | Actions |
---|---|---|---|---|
huang-integralsjumpdiffusionprocessesandmontecarlo.pdf | 2023-05-04 | Public | Download |