Mackevicius V. Stochastic Models of Financial Mathematics 2016 torrent

Textbook in PDF format

This book presents a short introduction to continuous-time financial models. An overview of the basics of stochastic analysis precedes a focus on the Black–Scholes and interest rate models. Other topics covered include self-financing strategies, option pricing, exotic options and risk-neutral probabilities. Vasicek, Cox-Ingersoll-Ross, and Heath–Jarrow–Morton interest rate models are also explored. The author presents practitioners with a basic introduction, with more rigorous information provided for mathematicians. The reader is assumed to be familiar with the basics of probability theory. Some basic knowledge of stochastic integration and differential equations theory is preferable, although all preliminary information is given in the first part of the book. Some relatively simple theoretical exercises are also provided.
Preface
Notations
Overview of the Basics of Stochastic Analysis
Brownian motion
Stochastic integrals
Martingales, Itô processes and general Itô’s formula
Stochastic differential equations
Change of probability: the Girsanov theorem
The Black–Scholes Model
Introduction: what is an option?
Self-financing strategies
Option pricing problem: the Black–Scholes model
The Black–Scholes formula
Risk-neutral probabilities: alternative derivation of the Black–Scholes formula
American options in the Black–Scholes model
Exotic options
Models of Interest Rates
Modeling principles
The Vašíček model
The Cox–Ingersoll–Ross model
The Heath–Jarrow–Morton model
Bibliography
Index
Back Cover