DERIVATIVES
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.
Intended learning outcomes
The course provides an in-depth understanding of financial derivatives — options, futures, forwards, and swaps — and their role in financial markets and risk management. Students will acquire the fundamental principles of derivative pricing, valuation, and hedging, including replication techniques and risk-neutral valuation, applying them to real-world contexts of market risk hedging and commercial exposures, while understanding the limitations of theoretical models. At the same time, they will develop strong quantitative and mathematical skills for modeling the underlying risk factors, through tools from mathematical analysis, probability, and the general theory of stochastic processes.
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
valuation, 'attendees': midterm 10/30, final exam (endterm 16/30 and individual seminar on a group project 4/30, total 2/3).
'Non attendees': one final exam only, which covers the entire program.
NB All exams, except for the projects, are written and open questions.
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
Early Exercise and Exotic Options: Bermudan and American options, lookback and barrier 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.