The aim of the course is to provide students with the basic of data and algorithms currently used in finance to price contracts.
Expected learning outcomes
Knowledge and understanding: The student must demonstrate knowledge of the techniques and mathematical tools used for the evaluation of financial contracts and actuarial risks.
Applying knowledge and understanding: The student should be able to apply the acquired knowledge to contracts evaluation problems and to be able to implement pricing models using the studied software tools.
Making judgements: the student should be able to use the acquired knowledge also in an autonomous way, by also applying them to other financial problems.
Communication: the student should be able to answer in a clear and thorough way to the questions of the oral examination.
Lifelong learning skills: the student should be able to show a good learning ability, by widening, for example, his/her knowledge with use of relevant bibliographic references.
Contents of calculus and Finance.
PART 1 (prof. De Marco): Advanced stochastic calculus and derivatives (24 hours). Stochastic calculus: probability spaces, random variables, stochastic processes, filtrations and adapted processes. Brownian motion. Stochastic differential equations. Stochastic integral. Ito's formula. Geometric Brownian motion. Martingales. Markets and the non-arbitrage principle. Complete markets. Self-financing portfolios. Markets governed by geometric Brownian motion. Black & Scholes equation. Delta hedging. The Feymann-Kac representation theorem. Solution of the Black & Scholes equation for call options.
PARTE 2 (prof.ssa Marino): Options (24 hours). Mechanics of options markets. Properties of stock options. Binomial trees. The Black and Scholes. Monte Carlo methods. Numerical methods for option pricing.
PART 3 (prof. De Marco): Introduction to risk theory. (24 hours) Choice under uncertainty. Expected utility and certainty equivalent. Insurance contracts and premium principles. Risk measures. Individual risk models. Collective risk models. Introduction to ruin theory.
During the lessons the issues mentioned in the study program will be discussed and presented. Additional teaching and support material is made available through the e-learning online platform Moodle, where slides presentation used at lesson can be found, together with additional material for deepening a number of thematic issues.
• The main readings will be suggested at the beginning of the course.
• J.C. Hull, Option, futures and other derivatives – Pearson
• R. Kaas, M Goovaerts, J Dhaene, M. Denuit, Modern Actuarial Risk Theory. Springer
• D. Luenberger, Investment Science.
• P. Bradimarte - Numerical Methods in Finance. A Matlab Based Introduction – John Wiley & Sons
• D. J. Higham, An Introduction to Financial Option Valuation, Cambridge University Press
The assessment is based on a written examination and a structured oral examination to evaluate the student's achievement of the learning objectives. The written examination consists in the resolution of 2/3 exercises. The time allocated for completion of the test (and exercises) is 1 hour and 30 minutes. During the test, the use of material provided by the teacher during the course and books is permitted.
The oral interview aims to evaluate the preparation on all topics covered by the program. At oral examination programs developed during the course for evaluating a financial contract will be discussed. Students should be able to show and illustrate the fundamental concepts acquired during their studies. The final mark is the average of the valuation obtained in the computer test, written exam and oral interview (equally weighted). The laude can be assigned is the student shows, that he or she is able, in the answers, to deepen the topics dealt with beyond what is stated in the reference texts and the materials presented in the lesson.