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
The contents of the courses Elementi di Probabilità and Probabilità.
Teaching Methods
Lectures about theoretical contents and interactive lectures where students will be called to solve some easy problems.
Assessment Methods
Oral examination. The questions will concern the topics developed during the lectures. The student will have to prove an appropriate knowledge and comprehension of the subject matter.
Texts
Introduction to Stochastic Calculus Applied to Finance, D.Lamberton e B. Lapeyre, Chapman&Hall/CRC
Contents
Introduction to some basic notions of 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). - 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). - Brownian motion and elements of stochastic calculus. - Pricing and hedging European options in the Black and Scholes' model. - Problems connected to asian and American options.
