Quantitative models for business management
Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
primo semestre lauree magistrali dal Oct 1, 2018 al Dec 21, 2018.
The aim of the lecture is to analyze the most important financial instruments typically employed for the management of interest rate and foreign exchange (FX) risk. Such risks influence the profitability of firms who are active on international markets. With this objective in mind, the first part of the lecture will introduce the necessary mathematical and statistica tools allowing the analysis of investment decisions in a context of uncertainty.
The second part will focus on financial instruments and related implementation aspects on the computer.
1) Mathematical preliminaires: probability theory, stochastic calculus and arbitrage free valuation.
2) Interest rate risk: financial instruments (zero-coupon bonds, forward rate agreements, interest rate swaps, caps, swaptions), interest rate curve bootstrapping, some aspects of term structure models.
3) Foreign exchange risk: introduction to FX markets, FX forwards, FX swaps, cross Currency swaps. FX options and their arbitrage free valuation. Long-dated FX products: hybrid FX-interest rate models.
1) A good working knowledge of mathematical analysis (limits/derivatives/integration). The ability to solve standard first and second order equations/inequations.
2) A good working knowledge of basic statistics (probability distributions, conditional probabilities, random variables, central limit theorem, law of large numbers, statistical tests, conditional/unconditional expected values/moments).
||Arbitrage theory in continuous time
||Oxford University Press
|Clark, I. J.
||Foreign Exchange Option Pricing: A Practitioner's Guide
||Term Structure Models: A Graduate Course
The exam consists of a 2-hour written test on all the topics in the program. The exam contains both theoretical and practical exercises. The ability to prove mathematical statements linked to the course material is expected.