Instructional goals
Introduction to Financial Derivatives: To familiarize students with the basic types of financial derivatives, including options, futures, forwards, and swaps.
Role and Functions of Derivatives: To understand how derivatives can be used for hedging, speculation, and arbitrage in financial markets.
Pricing and Valuation: To delve into the mathematical models and techniques used for pricing stock and interest rate derivatives.
Risk Management: To examine how derivatives can be used to manage various types of financial risk..
Real-World Applications: To analyze case studies and real-world examples of how financial derivatives are used in practice.
Prerequisites
An undergraduate Mathematical Finance course. A first year master's course (laurea magistrale) in Probability, with basic notions on stochastic processes
and stochastic calculus. A first year master's course in Mathematical Methods for Economics and/or Finance.
NB students from LUISS (undergrad + first year master's course) all possess these prerequistes.
Intended learning outcomes
Understanding Financial Derivatives: what financial derivatives are, their types (options, futures, forwards, swaps), and their role in financial markets.
Pricing, Valuation and replication: successful students will learn the fundamental principles of pricing and hedging financial derivatives, including the concept of no-arbitrage pricing and risk-neutral valuation.
Real World Applications: students will apply the concepts learned in the course to real-world situations, such as using derivatives for hedging currency risk in international business operations or understanding the limitations of the theoretical models.
Mathematical Skills: last but not least, students should develop the mathematical skills necessary to model underlying risk factors. This is crucial for pricing and hedging financial derivatives and includes calculus, probability, and statistics.
Course Contents
Valuation principles, interest rates and stock derivatives, Black Scholes model, models for interest rates, stochastic volatility.
Reference Books
Referenza principale:
Principles of Quantitative Finance, by I. Oliva and R. Renò. Apogeo ed. 2021.
Recommended book:
Options futures and other derivatives, by J. Hull, Prentice-Hall, any edition is fine.
Teaching Methods
Lectures, recitations, tutorials, class discussions. Meetings with practitioners.
Assessment Method
FEB valuation, 'attendees': problem sets, midterm, endterm and final seminar on a group project.
'Non attendees': one final exam only, which covers the entire program.
Thesis assignment criteria
Conversations with the professor.
Week 1
Term structure and parametric models for the construction of the zero curve. Common interest rate derivatives.
Week 2
Black Scholes model and European option valuation.
Week 3
Other considerations on European options, and the Greeks.
Week 4
American options.
Week 5
IR Derivatives with non linear payoff: caps, floors, and swaption. Black formula.
Week 6
Revision, midterm.
Week 7
Vasicek and CIR models fot the short rate.
Week 8
Limits of the B&S model. Analysis of the S&P 500, volatility surface.
Week 9
Discrete time models, stochastic volatility.
Week 10
Stochastic volatility models in continuous time.
Week 11
Hints on numerical pricing methods.
Week 12
Discussion with the students and feedback on the finalization of the group projects. Revision.