Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2019/2020
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 052500 - FINANCIAL ENGINEERING
Docente Baviera Roberto
Cfu 10.00 Tipo insegnamento Monodisciplinare
Didattica innovativa L'insegnamento prevede  2.0  CFU erogati con Didattica Innovativa come segue:
  • Cotutela con mondo esterno
  • Soft Skills

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

From theory to practice in finance. The course presents with a case-study approach some significant examples where a financial engineer could provide a relevant contribution:

  1. Credit Risk: single-name and multi-name products;
  2. Quantitative Risk Management (RM): from RM Measures to RM Techniques;
  3. Structured products: calibration, valuation and some hedging issues.


This teaching includes a version of 10 cfu, which is linked to a joint-course teaching by 8 cfu called FINANCIAL ENGINEERING (course 052505). This form defines objectives, programs and learning outcomes expected for both courses.

Risultati di apprendimento attesi

Both versions of the course have the following common learning goals:

1. to know and to understand

 -  fundamental risk measurement techniques (e.g. sensitivities, VaR, ES);

 -  their limits of applicability;

 -  some risk management techniques;

 -  single name and multi-name credit problems and models;

 -  main structured product typologies.


2. to apply this knowledge on some "Quantitative Case Studies" via the

 -  valuation of the relevant financial quantities (e.g. Net Present Value of some financial portfolios, risk measurement);

 -  calibration of underlying models;

 -  selection of an adequate risk management instrument/trading strategy.


It is expected an understanding by the student not limited to the definitions, the main results and the solution of standard exercises, but a critical knowledge able to discriminate different financial situations and a conscious model selection, justifying the chosen approaches.

Moreover the student should obtain correct solutions, explain adequately the codes, and expose properly the theory.

Argomenti trattati

0. Basic derivatives’ concepts

 -  Forward & option: Exchange-traded Markets vs OTC markets, Forward vs Futures. Forward Price: deduction via a no-arbitrage argument. European Option (Call/Put): decomposition in Intrinsic Value & Time Value; Put Call Parity. CRR & Black Model and examples. Monte-Carlo technique. 
 -  Main Greeks: Delta, Gamma, Vega e Theta. Volatility Smile.
 -  Basic Interest Rate (IR) instruments: Fundamental year-fractions in IR Derivatives. Depos, Forward Depos, FRA, STIR Futures, IR Swaps & Fwd Swap, Cap/Floor, Swaptions, “InterBank Floaters”.
 -  IR bootstrap. Sensitivities: BPV, DV01 and duration. For a linear portfolio, sensitivity analysis and hedging of IR risk with IRS.
1. Credit Risk
 -  Introduction to credit risk.
 -  Basic FI instruments in presence of Credit Risk: Fixed Coupon Bond, Floater Coupon Bond, Asset Swap, CDS. SPOL, CDS, ASW relations. Bootstrap Credit Curve.
 -  Firm-value (Merton, KMV calibration, Black-Cox) & Intensity Based Models (Jarrow & Turnbull, inhomogeneous Poisson).
 -  Multiname products (ABS, MBS, CDO) and models for HP and LHP (Vasicek).
 -  O'Kane & Schloegl model, double t-Student, General Threshold Model. 
 -  Copula approach and Li model with examples (Archimedean and Gaussian Copulas). 
 -  Implied Correlation in CDO trances.
2. Quantitative Risk Management
 -  Basel Accords, Risk Management Policy.
 -  VaR/ES: examples, Variance-Covariance method, Historical Simulation, Weighted Historical Simulation, Bootstrap, Full valuation Monte-Carlo, Delta-normal & Delta Gamma method, plausibility check, scaling rule.
 -  Coherent measures: assioms, VaR subadditivity (counterexample, elliptic case), ES coherence.
 -  Backtest VaR: Base approach, unconditional backtest, conditional backtest. [Only for 10 cfu version]
 -  Capital Allocation: Euler Principle & Contribution to VaR & ES.
3. Structured products main typologies with examples
 -  Certificates, Equity and IR Structured bond: the general Monte-Carlo approach for pricing non-callable structured products. Callable & Autocallable products.
 -  Deal structuring and Issuer hedging.
 -  Digital Risk: Slope impact & Black Correction in Autocallable products, FFT technique. Lewis formula for option pricing and analytic strip via an example: Exponential Levy model (NIG & VG). Global calibration and pricing via a Monte-Carlo (NIG & VG). Sticky Strike & Sticky Delta. Parsimony and smile symmetry.
 -  IR products and models: plain vanilla and exotics. HJM models: Main equation under Risk Neutral measure. Equivalence with a ZC bond approach and Fundamental Lemmas. Main examples:
  o   Market models: forward measure and application in the general derivative premium case. LMM and caplet solution. Calibration: Flat Vol vs Spot Vol in Cap/Floor markets.
  o   Hull White model (Extended Vasicek): Cap/Floors solution, Bond Options & Swaptions exact solution. Calibration issues. Pricing: Trinomial Tree Construction.
The 10 cfu version of the course (course 052500) uses some "Innovative teaching methods" designed and realized in collaboration with the financial industry (most of these methods are not included in the 8 cfu version, course 052505). Often this teaching methodology uses some "Quantitative Case Studies" that present some concrete problems for a financial institution, but simplified in order to be treated in a classroom. This approach requires the student to propose and realize quantitative solutions within a group (composed by 3 to 5 students) and with strict time constraints.  



It is advised to pass Mathematical Finance II before starting this course. In particular course presequisite are:

 -  Arbitrage Pricing Theory 
 -  Forwards, Futures, Call/Put European and American Options
 -  CRR and Tree pricing approach
 -  Floaters, Fixed Coupon Bonds and their sensitivities (e.g. duration)
 -  Stochastic Ito Calculus, Girsanov Theorem and change of measure
 -  Integration rules in the complex plain
 -  Proficiency in Matlab

Modalità di valutazione

The are five possible examination appeal dates, established in the academic calendar (two in June/July, one in September, two in January/February). Each exam appeal is composed by a written part and an oral part.

In the written part, the student is required to write:

 -  Matlab codes that solve some financial engineering problems;

 -  a document describing the chosen methodology, numerical results and problems/criticalities (if present).

The written and the oral part contribute to the final score with the same weight (15/30).

The examination appeal for the 8 cfu version, called FINANCIAL ENGINEERING (course 052505), does not include arguments specific of the 10 cfu version (both in the written and oral part).


The examination has the objective to verify whether the student has acquired the following skills:

1. The knowledge of

 -  fundamental risk measurement techniques (e.g. sensitivities, VaR, ES);

 -  their limits of applicability;

 -  some risk management and quantitative finance approaches;

 -  single name and multi-name credit problems and models.


2. The ability in applying the acquired knowledge in the computational/mathematical approaches for the

 -  calibration of financial models from real datasets;

 -  valuation/risk measurement/risk management of portfolios of elementary/structured products in presence of market and credit risks.

Risorsa bibliografica obbligatoriaA. J. McNeil, R. Frey & P. Embrects, Quantitative Risk Management: Concepts, Techniques and tools, Editore: Princeton University Press, Anno edizione: 2005, ISBN: 0691122555

Risk Management

Risorsa bibliografica obbligatoriaP.J. Schonbucher, Credit Derivatives Pricing Models, Editore: Wiley, Anno edizione: 2003, ISBN: 0470842911

Credit Risk

Risorsa bibliografica obbligatoriaJ. Hull, Options, futures and other derivatives, Editore: Pearson Prentice Hall, Anno edizione: 2009, ISBN: 0136015867

Software utilizzato
Nessun software richiesto

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 100:00 150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
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