Learning outcomes

The course is an introduction to the main theoretical models of quantitative finance with particular emphasis on the study of non arbitrage principle by introducing discrete and continuous time models. The course includes exercises on the arguments developed in MATLAB.

Prerequisites
Although no formal prerequisites for successful learning, it is recommended that you have already passed the test of Stochastic Models for finance in the first half.

Program

First part: The principle of non arbitrage and the derivatives pricing in discrete time

One period market. Arrow and Debreu securities. Portfolios of securities. Replicable securities. Complete and incomplete markets. Market equilibrium and arbitrage of the first and second kind. Non arbitrage principle and law of one price. Fundamental theorem of Finance (TFF). Risk neutral probabilities. Non arbitrage price of a security. Derivatives: definition and properties. Self financing portfolios. Multiperiod market: binomial tree model of Cox Ross and Rubinstein (CRR). Discret martingale processes. Risk neutral evaluation and replication of put and call options.

Second part: the principle of arbitrage and the derivatives pricing in continuous time

A market model in continuous time: the geometric Brownian motion. Stochastic calculus tools: stochastic differential equations. Continuous martingale processes. Normal and lognormal processes. Self financing portfolios. Replicable securities. Absence of arbitrage and completeness. Non arbitrage price of a title. Equivalent martingale measure. Girsanov's theorem. Feynman-Kac theorem. Black and Scholes Formula and its derivation. Delta hedging.

Textbooks
Teaching material is available online by accessing the e-learning page. Please refer also to the following books for the first part:
S. Pliska: Introduction to Mathematical Finance. Blackwell, 1997.
for thesecond part:
F. Menoncin: Mercati finanziari e gestione del rischio, Isedi, 2006.

Lessons
The lessons, for a total of 54 hours, are held in a classroom equipped with computers and dedicated software.

Examination Methods

The exam consists of a written test and an oral test. The written test consists in the resolution of four years. During the written test is allowed to use calculator only and you may not use lecture notes or other teaching material. Are allowed to take the oral test only students who have reported a mark greater than or equal to 16/30 in the written test.