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.