Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
primo semestre dal Sep 28, 2015 al Jan 8, 2016.
The course is prepared for students which 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.
1. Interest rate derivatives
a. Absence of arbitrage and risk-neutral probabilities
b. FRA, swaps
c. Black's model: caps, floors, swaptions
d. Short term models: Vasicek, CIR
e. Forward measure
f. The “double curve” model
2. Credit derivatives
a. Exponential distribution
b. Poisson processes
c. Reduced form models for credit risk
d. Risky bonds evaluation
e. Credit default swaps
f. Credit Valuation Adjustment
3. Equity derivatives
a. The limitations of the Black & Scholes model
c. Stochastic volatility in discrete time
d. Stochastic volatility in continuous time: Hull and White, Heston, SABR
e. Model free implied volatility: the VIX index
f. Multi-factor and jump-diffusion models
4. Derivati su valute
a. The Garman-Kolhagen formula
b. Currency swaps
c. Quotation methods
e. The Vanna-Volga model
Hull, Opzioni, Futures e altri derivati, Pearson Ed.
Brigo e Mercurio, Interest Rate Models-theory and Practice: With Smile, Inflation and Credit, Springer Ed.
Brigo, Morini, Pallavicini, Counterparty Credit Risk, Collateral and Funding, Wiley Ed.
Castagna, FX Options and Smile Risk, Wiley Ed.
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.