000516LM2 - MATHEMATICS FOR ECONOMICS: MODULE B

This module focuses on the application of discrete probability to discrete-time financial models. In particular, tree models for asset price evolution will be introduced and analyzed, with special attention to the Cox-Ross-Rubinstein binomial model and basic extensions. The course provides the foundations for understanding the principles of valuation and hedging of elementary derivative instruments.
EXPECTED LEARNING OUTCOMESStudents are expected to:


apply the fundamental concepts of discrete probability to the construction of tree models for asset prices;

use such models to analyze price dynamics and assess their implications in terms of arbitrage;

formalize and solve pricing problems related to elementary derivative instruments (European and American options);

understand the logic of discrete-time market models and be able to present it clearly;

develop simple theoretical arguments and proofs related to discrete-time valuation.

KNOWLEDGE AND UNDERSTANDINGBy the end of the module, students will have acquired knowledge of tree models for asset price evolution and their applications to the valuation and hedging of elementary derivative instruments, as well as an understanding of their main properties and implications.
MAKING JUDGEMENTSBy the end of the module, students will have developed the ability to critically analyze simple discrete-time financial models and to assess their consistency in terms of arbitrage and pricing.
COMMUNICATION SKILLSBy the end of the module, students will be able to clearly present the theoretical concepts and results learned, and to rigorously explain the reasoning underlying the solutions to problems and the applications to binomial and trinomial models.