Teaching code

4S02483

Teacher

Roberto Renò

Coordinatore

Roberto Renò

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

primo semestre (lauree magistrali) dal Oct 4, 2021 al Dec 17, 2021.

Lessons timetable Moodle Seminars

Learning outcomes

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.

Program

1. The Black and Scholes model
a. Absence of arbitrage and risk-neutral probabilities
b. Lognormal model
c. Option valuation
d. Hedging

2. Interest rate derivatives
a. FRA, swaps
b. Black's model: caps, floors, swaptions
c. Short term models: Vasicek, CIR
d. Currency options

3. Credit derivatives
a. Exponential distribution and stopping times
b. Reduced form models for credit risk
c. Risky bonds evaluation
d. Credit default swaps
f. Credit Valuation Adjustment

4. Stochastic volatility models
a. The limitations of the Black and Scholes model
b. Stochastic volatility in continuous time: Hull and White, Heston, SABR
c. Model free implied volatility: the VIX index

Bibliography

Examination Methods

** General

Written exam (70%) + Project Work (30%).
The Project Work, to be decided with the Teacher, is a small paper, with length less than 10 pages, dealing with one of the following jobs:
1) application of a model to market data
2) a simulation or numerical approximation of proposed models
3) the valuation of a contract involving derivatives
4) a valuable discussion of some part of the theory
5) the discussion of a recent scientific article
The Project Work needs to be completed to gain access to the written exam. It can be re-submitted. The final valuation will use the latest Project Work submitted.

** In case of sanitary emergency

In case the exam cannot be given because of sanitary emergency linked to the Covid-19 pandemic, the exam can be given in different forms, including online.