Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Derivatives (2024/2025)
Teaching code
4S02483
Teacher
Coordinator
Credits
9
Language
Italian
Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Period
Primo semestre LM dal Sep 30, 2024 al Dec 23, 2024.
Courses Single
Authorized
Learning objectives
The course is prepared for students who followed the courses “Stochastic Models for Finance” and “Mathematical Finance”. The Black-Scholes model is considered a prerequisite. The objective of the course is to describe and analyze the main mathematical models used for the valuation of financial derivatives. The course is divided into four pillars, which correspond to the four main financial markets: interest rate derivatives, credit derivatives, equity derivatives and FX derivatives. The course will also introduce practical tools for the implementation of the mathematical models with standard scientific software, and the calibration of these models to market data.
Prerequisites and basic notions
1. A good knowledge of basic mathematical analysis (limits/derivatives/integrals) and the ability to solve simple equations/inequalities.
2. Familiarity with the contents of stochastic methods for finance and mathematical finance. A good knowledge of basic statistics (probability distributions, conditional probabilities, random variables, central limit theorem, law of large numbers, statistical tests, conditional/regression and non-conditional expected values/moments).
3. Programming: the Java Finmath library will be used in the course. The attendance of the course "Introduction to programming in Java" is recommended
Program
1. Review of risk-neutral evaluation in continuous time.
2. Interest rate models and products
a. Derivative contracts linked to interest rates. Bootstrap reminders and risk management through curve trades.
b. Short rate models: Vasicek CIR, affine term structure. Deterministic shift extension.
c. Heath-Jarrow-Morton framework
d. Numéraire changes and forward measures
e. Market Models
f. Historical evolution of interest rate models: single curve setting, multiple curve, new benchmarks based on overnight rates.
3. Credit derivatives
a. Review of reduced-form models with deterministic intensity. to. Generalities on the intensity-based approach
b. Reduced form models for credit risk
c. Valuation of risky bonds
d. Credit default swaps
4. Stochastic volatility models
a. Black Scholes Formula Vs Black Scholes Model: volatility smile.
b. Local volatility: the Dupire formula
b. Continuous-time stochastic volatility models: Heston, SABR
c. Vanilla options pricing and Fourier transform calibration
d. Static replication of exotic options via portfolios of plain vanilla options
5. (Optional Topic) Overview of FX products and their use
a. FX forwards and FX Swaps
b. Cross Currency Swaps
c. FX Options
d. Long-Dated FX: Power Reverse Dual Currency Notes and Hybrid FX Rate Models.
Bibliography
Didactic methods
Standard lectures and programming sessions.
Learning assessment procedures
The exam consists of two parts: the first is a Project Work that has to be completed by using the Java programming language. The mark on the project work has a weight of 30% on the final grade.
The Project Work can be completed by groups consisting of up to 4 people.
Aims of the project work are:
implement and deepen the understanding of the methods illustrated during the lecture.
improve the ability to work in teams.
The grade of the project work has unlimited validity.
Students get access to the written exam only if the project work has a positive valuation. Those who do not submit any solution will receive the mark 0/30.
The second part of the exam consists of a written exam on all topics of the lecture. The exam contain theoretical and practical exercises together with programming questions related to the Java programming language. In case the grade is greater or equal to 18, the written exam has a weight of 70% on the final mark.
Evaluation criteria
Level of knowledge of the course material. The ability to apply the theory via theoretical and programming exercises also in contexts which have not been perfectly covered during the lecture.
Criteria for the composition of the final grade
30% PW + 70% Final Exam if approved (see details in the section above)
Exam language
Italiano o inglese
