Course: Financial Engineering
Main obiectives and contents
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.
Description of main arguments
1. 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, Interest Rate 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.
2. 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.
3. Quantitative Risk Management
- Basel I & II, 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, losses over Several Periods and Scaling rule. Coherent measures: assioms, VaR subadditivity (counterexample, elliptic case), ES coherence.
- Backtest VaR: Base approach, unconditional backtest, conditional backtest.
- Capital Allocation: Euler Principle & Contribution to VaR & ES.
- Incremental Risk Charge.
4. Structured products main typologies with examples.
- 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. Proposition: Equivalence with a ZC bond approach. Fundamental Lemmas and 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.
- Arbitrage Pricing Theory
- Forwards, Futures, Call/Put European and American Options
- CRR and Tree pricing approach
- Fixed Coupon Bonds, Floaters and their sensitivities (e.g. duration)
- Stochastic Ito Calculus, Girsanov Theorem and change of measure
- Integration rules in the complex plain
- Proficiency in Matlab