Obiettivi formativi
This course is about how derivatives across fixed-income, equity, and credit markets are priced, traded, and used by market participants for hedging, investment, and risk management. It emphasises a small number of powerful ideas — no-arbitrage, replication, and risk-neutral valuation — and applies them systematically across instrument classes, from interest rate swaps and credit default swaps to equity options and structured products.
The course combines rigorous theoretical foundations with direct exposure to professional market practice, including how derivatives are quoted and traded in real markets. The goal is to bridge the gap between academic valuation frameworks and their day-to-day application in the derivatives industry.
Risultati di apprendimento attesi
Upon successful completion of this course, students will be able to:
• Understand and apply the no-arbitrage principle and risk-neutral valuation as unifying frameworks across asset classes.
• Master the mechanics of the core derivative instruments across fixed-income, equity, and credit markets, as well as the modern XVA pricing framework.
• Understand how derivatives are quoted, priced, and traded in real markets on Bloomberg for both OTC and listed instruments.
• Use derivatives for hedging, trading, investment, and risk management purposes.
• Critically assess model assumptions and recognize how frictions — collateral, funding, central clearing — impact derivative valuations.
• Implement pricing models using Python and Excel.
• Apply the acquired competences in professional contexts such as derivatives trading, asset management, risk management, and financial structuring.
Prerequisiti
Students are expected to have a solid understanding of:
• Financial mathematics
• Probability and statistics
• Calculus (derivatives, integrals)
• Excel
Prior exposure to Python programming is recommended but not required.
Contenuti Del Corso
The course is organized in two blocks.
The first block (Weeks 1–6) covers fixed income and credit derivatives: no-arbitrage foundations, yield curve construction, interest rate derivatives (FRAs, swaps, caps/floors, swaptions), credit derivatives (CDS, CDS indices), and short-rate term structure models (Vasicek, CIR, Hull–White).
The second block (Weeks 7–12) covers equity derivatives and counterparty risk: risk-neutral pricing, the Black–Scholes framework, Greeks, dynamic hedging, exotic options, structured products, counterparty credit risk (CVA/DVA), and the XVA framework (FVA, MVA, KVA).
Testi Di Riferimento
• Hull, J.C. (2022). Options, Futures, and Other Derivatives, 11th Ed., Pearson.
• Wilmott, P. (1998). Derivatives: The Theory and Practice of Financial Engineering. Wiley.
• Wilmott, P. (2007). Paul Wilmott Introduces Quantitative Finance, 2nd Ed., Wiley.
• Gregory, J. (2026). The xVA Challenge: Counterparty Risk, Funding, Collateral, Capital and Initial Margin, 5th Ed., Wiley.
Metodologie Didattiche
• Lectures and in-class discussions
• Bloomberg terminal demonstrations for pricing, quotation, and trading of OTC and listed derivatives
• Hands-on exercises (Excel and Python)
• External materials (academic papers, market reports)
Modalità di verifica dell'apprendimento
Attending students:
Midterm exam (1/3 of the final grade): a written exam covering the material from Weeks 1–6, consisting of a mix of multiple-choice theoretical questions and exercises. The midterm grade is mandatory and cannot be refused.
Final exam (2/3 of the final grade): a written exam covering the entire course syllabus, consisting of a mix of multiple-choice theoretical questions and exercises. The combined midterm + final grading applies only to the examination sessions at the end of the semester in which the course is taught. In subsequent sessions, students are evaluated through a single final examination (100%).
Non-attending or exempted students:
A single written examination covering the full course syllabus (100%), consisting of a mix of multiple-choice theoretical questions and exercises.
Failure to achieve a minimum score of 18/30 results in a failing grade. Correct answers to all questions and excellent execution of all exercises will result in a grade of 30/30 cum laude.
Criteri per l’assegnazione dell’elaborato finale
• Submission of a research proposal (max 1 page)
• Discussion with the instructors
• Relevance to course themes
• Minimum grade achieved in this course: 27/30
• Instructor supervision availability
Settimana 1
No-Arbitrage and Term Structure Foundations
No-arbitrage principle; discount factors; forward rates; bootstrapping the zero curve; risk-neutral valuation in fixed income context.
Readings: Hull Ch. 1–4.
Settimana 2
Interest Rate Derivatives
Forward Rate Agreements (FRAs); interest rate futures (SOFR/Treasury); duration and convexity; hedging interest rate risk.
Readings: Hull Ch. 4–6.
Settimana 3
Swaps and Multi-Curve Framework
Interest rate swaps (IRS): pricing and market conventions; marking-to-market; cross-currency swaps; OIS discounting; collateral impact on pricing.
Readings: Hull Ch. 7; selected material on multi-curve framework.
Settimana 4
Interest Rate Options
Bond options; caplets and floorlets; valuation of caps and floors; European swaptions; Black’s model on the swap rate; volatility conventions and hedging.
Readings: Hull Ch. 29.
Settimana 5
Credit Risk and Credit Derivatives
Structural vs reduced-form models; hazard rates; bootstrapping the credit curve; CDS pricing and market conventions; CDS indices.
Readings: Hull Ch. 24–25; Gregory Ch. 1–3.
Settimana 6
Short-Rate and Term Structure Models
Equilibrium models (Vasicek, CIR); no-arbitrage models (Ho–Lee, Hull–White); calibration to initial term structure; multiple yield curves.
Readings: Hull Ch. 30–32 (selected).
Settimana 7
Risk-Neutral Pricing and GBM (Equity Context)
Binomial tree (Cox–Ross–Rubinstein) and convergence to continuous time; Geometric Brownian Motion and its limitations; Ito’s Lemma; change of measure (Girsanov); risk-neutral valuation for equity derivatives; choice of numeraire.
Readings: Hull Ch. 1–6; Wilmott (GBM, Ito).
Settimana 8
Black–Scholes and Dynamic Hedging
Derivation of the Black–Scholes PDE; closed-form pricing of European options; the full Greeks (delta, gamma, vega, theta, rho); implied volatility, smile and skew; dividends and forwards; dynamic hedging in practice and its frictions (transaction costs, gap risk, jumps).
Readings: Hull Ch. 13–18; Wilmott (Black–Scholes).
Settimana 9
Advanced Equity Derivatives
American options (early-exercise and Bermudan structures); barrier and digital options; Asian options (arithmetic vs geometric); local volatility (Dupire) vs stochastic volatility (Heston); equity exotics (autocallables, cliquets) and retail vs institutional structured products.
Readings: Hull Ch. 25–27; Wilmott (Exotics).
Settimana 10
Counterparty Credit Risk
Exposure profiles (EPE, ENE, PFE); bilateral CVA and DVA; wrong-way risk (specific vs general); ISDA netting and CSA mechanics; collateral haircuts; close-out conventions and termination.
Readings: Gregory Ch. 4–7.
Settimana 11
XVA Framework and Modern Pricing
FVA (Funding Valuation Adjustment); MVA (Margin Valuation Adjustment); KVA (Capital Valuation Adjustment); the central clearing transformation; the FVA debate (Hull–White vs Burgard–Kjaer); XVA aggregation and trading desks; regulatory capital implications (SA-CCR, IMM).
Readings: Gregory Ch. 8–12.
Settimana 12
Integrated Case Studies in Modern Derivatives Pricing
Multi-curve pricing architecture (OIS-discounting and projection curves); equity-credit hybrid structures; wrong-way risk in structured products; central clearing vs bilateral pricing; practical case studies drawn from recent market events (Archegos collateral failure, LDI gilt crisis 2022, Credit Suisse AT1 write-down).