Learning objectives
The course will consist of a blend between theory and practice of the most popular numerical methodologies used in the quantitative desks of financial institutes. The course is intended as a continuation of the Financial Mathematics module, with particular attention to implementative and practical aspects.
a)Understanding skills and acquired knowledge
At the end of the course, the student will understand the need for financial models going beyond the classic Gaussian paradigm; will be able to implement in MATLAB the most popular alternatives to the Black-Scholes model and the associated hedging strategies, and will be able to understand the origin and nature of the volatility surface.
b) Ability of applying the acquired knowledge
The student will be able to employ the learned techniques to work on the most important financial markets indicators, as well as exotic products, both under a theoretical and applied side.
c) Independence of judgement
The student will be capable of assessing critically the circumstances under which some given mathematical models work better than others, and define their potential and limitations.
d) Communication skills
The student will learn relevant methodologies to solve common modelling problems in finance
e) Learning abilities
The offered combination of theory followed by immediate applications, will hold firm the intuition of the student to the idea that advanced methods in finance do not form a body of abstract theory, but answer needs and find application in concrete financial problems.
Prerequisites
It is absolutely necessary to have attended the Financial Mathematics module. Some proficiency in MATLAB is also expected.
Course unit content
Volatility surface. Local volatility and the Dupire Equation. Stochastic volatility models with and without jumps. Delta, Vega and Gamma hedging. Robustness of the Black-Scholes formula. American option pricing using trees. Other selected topics in quantitative finance and risk management.
Full programme
Bibliography
The main references will be pointed to during the course and, together with lecture notes, made available on the ELLY online system.
Teaching methods
Classroom lectures and laboratory demonstration. The lectures will be divided between theoretical explanations, MATLAB code illustration, and possible exercises related to the examples provided. The MATLAB code will be uploaded on the ELLY online system before the beginning of the course.
Assessment methods and criteria
The students, working alone or in groups, are assigned a research topic similar to those treated during the lectures, and will have to prepare a programming exercise. These will be then discussed during a classroom seminar. Cum laude marks will be attributed to those students who will show deeper understanding and ability of critical assessment in the theoretical aspects of the subject matter, as well as performing an outstanding implementation of the programming exercise.
The University will send to the students an email message to their University email address with the result of the exam (through the Essetre system). The students are allowed to reject the grade within a week from the receipt of such a message through an online procedure.
Other information
