Students will have to achieve the following objectives: - understand some basic notions about the applications of probability theory and stochastic processes to finance, - know the fundamental mathematical objects for describing a financial market and understand their use, - be able to explain key concepts and results, and discuss their connections, - be able to illustrate the proofs of the main results.
Course Prerequisites
Contents of the course “Probability and Stochastic Processes” are necessary by didactic regulation (Art.10). This means that, in order to sign in for the “Quantitative Finance” exam, it is necessary to pass the “Probability and Stochastic Processes” exam.
Teaching Methods
Lectures about theoretical contents and interactive lectures where students will be called to solve some problems and exercises.
Assessment Methods
The exam is both written and oral and will focus on topics covered in class. The written test involves solving exercises and answering theoretical questions. The student must achieve a minimum score of 16 out of 30 on the written test in order to proceed to the oral exam. In the oral exam, students are required to demonstrate their understanding of the topics, communicate their knowledge effectively, and engage in discussions about connections and applications. Some activities that allow for a bonus on the final grade will be presented at the beginning of the course.
Texts
Introduction to Stochastic Calculus Applied to Finance, D.Lamberton e B. Lapeyre, Chapman&Hall/CRC
Contents
Introduction of some basic notions in mathematical finance: markets, options, strategies, options' pricing and hedging. Study of some main properties of markets in a discrete setting and of the Black and Scholes' model. Extended summary: - Quick resume of some probabilistic tools (conditional expectations and martingales, in particular), Brownian motion and elements of stochastic calculus. - Definitions of basic objects used in mathematical finance: options, markets, strategies, arbitrage... - Pricing and hedging european options in discrete models (with discrete times and discrete probability space). - Pricing and hedging European options in the Black and Scholes' model. - Problems related to non European options.
