Financial Engineering

FINANCIAL ENGINEERING (Master Level, Mathematical Engineering)
Prof. Roberto Baviera in collaboration with dr. Emanuele Mercuri (Illimity) & dr. Aldo Nassigh (Unicredit) and also Prof. Michele Azzone & dr. Pietro Manzoni (PoliMi).

Main obiectives and contents
From theory to practice in finance with a case-study approach:
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.

Suggestions by previous year students (before starting the course) can be found below. Pls check also for course prerequisites.


Description of main arguments

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, FRA, STIR Futures, Interest Rate Swaps & Fwd Swap, Cap/Floor, Swaptions.
  • IR bootstrap. Sensitivities: BPV, DV01 and duration. Sensitivity analysis and hedging of IR risk with IRS.

1. Credit Risk

  • Introduction to credit risk.
  • Basic Fixed Income 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 models (Jarrow-Turnbull, inhomogeneous Poisson).
  • Multiname products (ABS, MBS, CDO) and models for HP and LHP.
  • Copula approach and Li model with examples (Archimedean and Gaussian Copulas), CDO Implied Correlation.

2. Quantitative Risk Management

  • Basel Accords, Risk Management Policy.
  • VaR/Expected Shortfall (ES): Variance-Covariance method, Historical Simulation, Weighted Historical Simulation, Bootstrap, Full valuation Monte-Carlo, Delta-normal & Delta Gamma method, plausibility check and Scaling rule. Coherent measures: assioms, VaR subadditivity (counterexample, elliptic case), ES coherence.
  • Backtest VaR: Basel approach, unconditional & conditional backtest.
  • Capital Allocation: Euler Principle & Contribution to VaR & ES.

3. Structured products

  • Certificates, Equity and IR Structured bond: the general Monte-Carlo approach for pricing not-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 and characteristic function (NIG & VG). Global calibration and pricing via a Monte-Carlo (NIG). 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. Fundamental Lemmas and examples:
    o Market models: BMM, LMM and SMM. Calibration: Flat Vol vs Spot Vol in Cap/Floor markets.
    o Hull White model (Extended Vasicek): Cap/Floor & Swaption solution. Calibration. Pricing: Trinomial Tree.

Course Prerequisites
Mathematical Finance II, Stochastic Differential Equations and (proficiency in) Matlab
More in detail:
– Arbitrage Pricing Theory
– Forwards, Futures, Call/Put European and American Options. Physical delivery & Cash settlement
– CRR and Tree pricing approach
– Fixed Coupon Bonds, Floaters and their sensitivities (e.g. duration), caplet/floorlet and swaption
– Filtration, Stochastic Ito Calculus, change of measure and Girsanov Theorem, Stochastic Fubini-Tonelli theorem
– Integration rules in the complex plain
– Proficiency in Matlab

Course organization
– Written & oral examination
– The 10 CFU version uses some “Innovative teaching methods” designed in collaboration with the financial industry.
   This version could end also with a final project; starting from the AY 2019-2020 the best pitch has been awarded. Also a second and a third edition of the Best Pitch Award has been conferred for the AY 2020-2021 and AY 2021-2022. Last but not least, it has been followed by a fourth edition for the AY 2022-2023.


Suggestions (and answers to some FAQs) by previous year students: “Should I choose FE?”

… and do not hesitate to contact previous years’ students for any further question and/or clarification!

1. J. Hull (2009), Options, futures and other derivatives, Pearson Prentice Hall, 7th Ed.
2. A.J. McNeil, R. Frey, P. Embrects (2005), Quantitative RM: concepts, techniques and tools, Princeton Univ. Press
3. P.J. Schonbucher (2003), Credit Derivatives Pricing Models, Wiley

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