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.
Obiettivi Formativi
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
derivative securities
Prerequisiti
We assume some familiarity with probability theory