Cálculo Estocástico e Aplicações às Finanças

Objectives

Available soon

General characterization

Code

11579

Credits

6.0

Responsible teacher

Maria Fernanda de Almeida Cipriano Salvador Marques

Hours

Weekly - 4

Total - Available soon

Teaching language

Português

Prerequisites

Available soon

Bibliography

1 -- Hui-Hsiung Kuo: Introduction to Stochastic Integration. Springer. 2006

2 -- Bernt Oksendal: Stochastic Differential Equations. Sringer. 1998

Teaching method

Available soon

Evaluation method

Available soon

Subject matter

1- Stochastic Integral


2-Itô Formula


3 - Stochastic differential equations (existence and uniqueness theorem)

4- Solving linear equations.

5- Markov''''''''s property of the solution of a stochastic differential equation.

6- Forward and backward Kolmogorov''''''''s equations 

7- Girsanov''''''''s Theorem

8- Martingale representation theorem.


9- Black-Sholes Model

9.1- martingale measure

9.2- Replication strategy.

9.3- Price of European options

9.4- Black-Scholes Equation

9.5- Price of barrier options

9.6 Price of American options

9.7- Price of an America option as a solution to a free boundary problem.

10- Introduction to Malliavin Calculus

10.1- Study of price sensitivity using Malliavin''''''''s calculation

Programs

Programs where the course is taught: