Marco Marchioro

Learning Quantitative Finance with QuantLib

Interest Rate Derivatives Lectures (a.a. 2012/2013)

Interest rates 1: Introduction to exotic derivatives (October 6th, 2012)

- Introduction to module "Interest Rate Derivatives" as part of class "Advanced Derivatives"
- A real-life example of an exotic derivative
- Structure of a derivative term sheet
- Pricing tools and pricing software
- QuantLib: an open-source tool
- QuantLibXL: using QuantLib on a spreadsheet
- Object handler and defining objects on a spreadsheet
- Day counters, business calendars, and end-of-month conventions

⁃ Examples using QuantLibXL

Revised QuantLibXL XLL: QuantLibXL-vc90-mt-1_1_0.xll

PDF file: lecture01_slides.pdf, Spreadsheet: Class-01.xls, XML example: L01-PRICEFUNCS-106.xml

Interest rates 2: Linear Interest Rate Derivatives (October 13th, 2012)

- Interest-rates: definitions
- Compounding conventions: simple, compounded, continuous
- Money-market account
- The discount factor
- Yield curve described by a single rate
- Interbank deposit and deposit rates

- Forward-rate agreements (FRA)
- Interest-rate futures
- Interest-rates swaps
- IRS fixed leg, IBOR leg, and fair swap rate

PDF file: lecture02_slides.pdf, Spreadsheet: L02-Exercises.xls, External material: External-Material.pdf

Reference paper: Pricing Simple Interest-Rate Derivatives

Interest rates 3: Bootstrapping the interest-rate term structure (October 20th, 2012)

- Market quotes of deposit rates, IR futures, and swaps
- Need for a consistent interest-rate curve
- Instantaneous forward rate
- Interest-rate term structure built using multiple rates
- Bootstrapping quoted deposit, futures, and swap rates
- Foreign-exchange forward contract
- Sensitivities of interest-rate portfolios (DV01)
- Hedging portfolio interest-rate risk

PDF file: lecture03_slides.pdf, Spreadsheet: L03.xls

Reference paper: Pricing Simple Interest-Rate Derivatives

Interest rates 4: Vanilla interest rate options (October 27th, 2012)

- Probability evolution at information arrival
- Brownian motion and option pricing
- Probability measures: physical and risk neutral
- Interest-rate options, Caplets and Black formula
- Caps, Floors, and Collars. Cap/Floor parity
- Bootstrap of volatility term structure cap volatilities
- Options on swaps (Swaptions)
- Historical and implied volatilities
- Volatility smile
- Caps and floors with digital payoffs or with barriers

PDF file: lecture04_slides.pdf, Spreadsheet: L04-InterestRateDerivatives.xls,

Interest rates 5: Exotic interest-rate options (November 10th, 2012)

- Exotic caps, floors, and swaptions
- Swaps with exotic floating-rate legs
- Commodities and no-arbitrage
- Numeraires and pricing formulas
- Stochastic differential equations (SDEs)
- Partial differential equations (PDEs)
- Feynman-Kac formula
- Numerical methods: analytical approximations

PDF file: lecture05_slides.pdf

Interest rates 6: Equilibrium interest-rate models (November 17th, 2012)

- Bond options
- Introduction to interest-rate models
- Short-rate models
- Equilibrium models: Vasicek model
- Other equilibrium models
- Binomial and trinomial trees
- Finite differences

PDF files: lecture06_slides.pdf

Interest rates 7: Market interest-rate models (November 24th, 2012)

- No-arbitrage models
- Hull-White model
- Monte Carlo simulations
- Libor market model
- Other market interest-rate models

PDF file: lecture07_slides.pdf

Credit derivatives 1: Introduction to credit risk (December 1st, 2012)

- Corporate bonds, asset swaps, and z-spreads
- Risky yield curves
- Risk-less yield curve
- Definition of credit derivatives
- Comparison with other derivatives
- Survival and default probabilities, hazard rates
- Credit default swap, spread, and upfront quotes
- Standard definitions of default, restructuring, and seniority
- Bootstrap of probability curve from quoted CDS
- Example of quoted CDS spreads
- Credit risk hedging using credit-default swaps
- Some historically important recovery ratios

PDF file: credit01_slides.pdf

Reference paper: Pricing Simple Credit Derivatives

Revised QuantLibXL XLL: QuantLibXL-vc90-mt-1_1_0.xll

Examples: L07-creditdefaultswap_1.xml, L07-RR-truvo-21092010.pdf, L07-creditdefaultswap_1.pdf, L07-Standard.CDS.Contract.Specification.2009-05-12.pdfCredit derivatives 2: Financial instruments with credit risk (December 15th, 2012)

- Example of quoted CDS spreads
- Credit risk hedging using credit-default swaps
- Some historically important recovery ratios
- Exotic single-name credit derivatives
- Portfolio credit derivatives
- Credit-default-swap index
- Major traded indexes

PDF file: credit02_slides.pdf, SOV CDS SOV-cds-spread-2012-12.xlsx, Example: L08-itraxx-europe-series-13.pdf

Reference paper: Pricing Simple Credit Derivatives

Credit derivatives 3: Advanced credit derivatives (Extra Material)

- Asset-backed securities
- Simple model for ABS pricing
- Mortgage-backed securities
- Collateralized debt obligations (CDOs)
- Credit derivatives and the 2007-2008 market crisis

PDF file: credit03_slides.pdf

Reference papers: Average-maturity Model for Asset Backed Securities, Pricing Simple Credit Derivatives

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