Probability.Stochastic processes in discrete and continuous time. Bownian motion, Ito formula, martingale.
The Black-Scholes model.The Cox-Ross-Rubinstein model.Pricing:The no-arbitrage price and its implications. The Black- Scholes PDE pricing formula for European options. Risk neutral valuation. Hedging: the Greeks. Pricing of American Options. Path dependent options.Some extensions of Black-Scholes model. Stochastic volatility models. Jump-diffusion models.
The term structure.
J. Hull, Options, Futures and other Derivative Securities. Prentice Hall.
T.Bjork, Arbitrage theory in continuous time. Oxford University Press.
The course will present some fundamental quantitative tools for the analysis of financial markets. We will study a set of models which describe the evolution over time of securities' prices, both with discrete time models, and with continuous time models. Further we will discuss the issue of pricing and hedging of
Calculus and Integration
Classes and exercises
Type of Assessment
It is given as a written exam. This is intended to verify: 1) the acquired knowledges as for concepts, models and tools which have been the object of the course; 2) the following skills have been developed by the student: ability to apply the knowledges obtained, ability to derive conclusions, communication skills using an adequate language, understanding and learning ability.
30% Test about Probability
70% Final written exam