Finanças Quantitativas

Objectives

This course is focused on the mathematical models used to price securities and measure risk. By learning the fundamentals of stochastic calculus, the students are able to understand and derive the price of derivatives using the Black-Scholes model. Furthermore, the students are introduced to the basics of Real Options Analysis, which is then used in the valuation of real options concerning business investment opportunities - options to expand, change, or curtail projects based on changing economic, technological, or market conditions.

Syllabus

Chapter 1: Option pricing a. Introduction and Revision about basic concepts (interest rates, derivatives); b. Arbitrage; c. First properties of option pricing (bounds on option pricing; put-call parity); d. Replicating Portfólios. Chapter 2: Stochastic Calculus a. Brownian motion and diffusions; b. Ito's integral; c. Ito's formula Chapter 3: Black-Scholes formula a. Assumptions and discussing; b. Black-Scholes equation; c. Option pricing via replicating portfolios; d. Implicit volatility. Chapter 4: Real options a. Definition of the problem; b. Dynamical Programming Principle; Hamilton- Jacobi-Bellman equations; b. Standard solution for an investment or exit problem; c. Other questions.

Prerequisites

The students must have followed a course on Probability and Statistics, and have basic notions about interest rates and derivatives.

Cross Competence Component

• Critical and Innovative Thinking (e.g. creativity, strategic thinking, approaches to problem solving); 6% • Interpersonal skills (eg oral presentations, communication and organizational skills, team work, etc.): 6% • Intrapersonal Skills (eg self-discipline, enthusiasm, perseverance, self- motivation, etc.): 6% • Global Citizenship (e.g. tolerance, openness, respect for diversity, intercultural understanding, etc.): 6% • Information and media literacy (including the ability to locate and access information, as well as to analyze and evaluate media content): 6%

Ethical Principles

All members of a group are responsible for the group’s work. In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.