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ISCTE-IUL  >  Education  >  MMF

Stochastic Calculus in Finance I (2 º Sem 2019/2020)

Code: M7601
Acronym: M7601
Level: 2nd Cycle
Basic: No
Teaching Language(s): Portuguese
Friendly languages:
Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.
1 7.0 22.0 h/sem 10.0 h/sem 0.0 h/sem 0.0 h/sem 0.0 h/sem 0.0 h/sem 0.0 h/sem 32.0 h/sem 164.0 h/sem 0.0 h/sem 196.0 h/sem
Since year 2019/2020
Pre-requisites No
Objectives Knowledge of the main probabilistic tools used for pricing financial derivatives.
Program 1. Basic notions of Probability Theory.
2. Conditional Expectation.
3. Discrete-time Martingales.
4. Continuous time stochastic processes.
5. Brownian motion.
6. Itô´s stochastic integral.
7. Itô formula.
8. Martingale representation theorem.
9. Stochastic differential equations.
10. Girsanov theorem.
11. Feynman-Kac formula.
Evaluation Method Regular grading system:
- One individual exam
Students that fail or want to improve their grade in the regular grading system have one additional moment to pass: a re-sit exam, that is worth 100% of the final grade.
In any of the evaluation systems (regular or re-sit exam) it is considered that a student has course approval if he has a grade equal or above 9.5 points.
Teaching Method The student should acquire analytical, information gathering, written and oral communication skills, through the following learning methodologies (LM):
1. Expositional, to the presentation of the theoretical reference frames
2. Participative, with analysis and resolution of application exercises
3. Active, with the realization of individual works
4. Self-study, related with autonomous work by the student, as is contemplated in the Class Planning.
Observations
Basic Bibliographic Isabel Simão, Cálculo Estocástico em Finanças I, Texto de apoio às aulas, 2006.
Complementar Bibliographic -D. Lamberton and B. Lapeyre, Stochastic Calculus Applied to Finance, Chapman and Hall/CRC, 1996.
-T. Mikosch, Elementary Stochastic Calculus with Finance in View, World Scientific, 1998.
-B. Oksendal, Stochastic Differential Equations and Applications, Springer-Verlag, 5a  edição, 1998.