Master’s degree in Banking and Finance


Course code
Name of lecturer
Roberto Renò
Roberto Renò
Number of ECTS credits allocated
Academic sector
Language of instruction
primo semestre lauree magistrali dal Oct 1, 2018 al Dec 21, 2018.

Lesson timetable

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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.


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 b. Greeks 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 d. Exotics e. The Vanna-Volga model Textbook: Hull, Options Futures and Other Derivatives, Pearson Ed. Additional reading: 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.

Reference books
Author Title Publisher Year ISBN Note
HULL J. Opzioni, futures e altri derivati (Edizione 8) Pearson Education Italia, Prentice Hall, Milano 2012 9788871927794

Assessment methods and criteria

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.

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