Marco Marchioro

Learning Quantitative Finance with QuantLib

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

This page will be updated with the lecture slides, the study material, and the spreadsheets needed for the class. The updated QuantLib add-in xll file can be found at this link. We have a temporary calendar for this year.

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

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

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.xmlL07-RR-truvo-21092010.pdfL07-creditdefaultswap_1.pdfL07-Standard.CDS.Contract.Specification.2009-05-12.pdf

Credit 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 SecuritiesPricing Simple Credit Derivatives

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