These lecture notes are based on a graduate course given for several years at Vilnius University as part of the master program Financial and Actuarial Mathematics. They are intended to give a short introduction to continuous-time financial models including Black--Scholes and interest rate models. Some basic knowledge of stochastic integration and differential equations theory is preferable, although, formally, all the preliminary information is given in part 1 of the lecture notes. About continuous-time stochastic models of financial mathematicsBlack-Sholes model and interest rate modelsRequiring a minimum knowledge of stochastic integration and stochastic differential equations INDICE: OVERVIEW OF THE BASICS OF STOCHASTIC ANALYSIS 1. Brownian motion 2. Stochastic integrals 3. Martingales, It's processes and general It's formula 4. Stochastic differential equation 5. Change of probability: The Girsanov theorem THE BLACK-SCHOLES MODEL 6. Introduction: what is an option? 7. Self-financing strategies 8. Option pricing problem: The Black-Scholes model 9. The Black-Scholes formula 10. Risk-neutral probabilities. Alternative derivation of Black-Scholes formula 11. American options in the Black-Scholes model 12. Exotic options MODELS OF INTEREST RATES 13. Modeling principles 14. The Vasi?cek model 15. The Cox-Ingersoll-Ross model 16. The Heath-Jarrow-Morton model
- ISBN: 978-1-78548-198-7
- Editorial: ISTE Press - Elsevier
- Encuadernacion: Cartoné
- Páginas: 130
- Fecha Publicación: 12/10/2016
- Nº Volúmenes: 1
- Idioma: Inglés