Term Structure Modelling and Interest Rate Option Pricing

Day One

09.00 - 09.15 Welcome and Introduction

09.15 - 12.00 The Term Structure of Interest Rates

• The Term Structure and its Applications
• Factors Explaining Shape of Term Structure
• Brief Review of Term Structure Estimation Techniques

Modelling Volatility

• Definition of Volatility
• Types of Volatility
• Standard Approach to Estimating Volatility
• Check for Normality of the Returns
• Possible Explanations for the Fat Tails
• Moving Averages
  • Simple moving average
  • EWMA
  • Attractions of EWMA
  • The EWMA as special case of the GARCH process
• Examples and exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Modelling Volatility (Continued)

• GARCH Modelling
  • Introduction
  • General model appearance
  • Conditional and unconditional variance
  • GARCH (1,1)
  • Higher order GARCH
• Implementing GARCH
  • Variance targeting
  • Maximum Likelihood Methods
• Forecasting Future Volatility
• Volatility Term Structures
• Combining GARCH with EVT-theory to Capture Fat Tails
• Modelling Correlations
• Volatility Clustering and Correlations
• Examples and exercises

Day Two

09.00 - 09.15 Recap

09.15 - 12.00 Term Structure Models

• Introduction to Interest Rate Models
• Features of Interest Rate Models
  • One or two factors
  • No-arbitrage
  • Mean reversion
  • Spot or forward rates
• Equilibrium Models
  • Rendleman and Barter
  • Vasicek
  • Mean reversion in the Vasicek model
  • Term structures in the Vasicek Model
  • Cox, Ingersoll, & Ross (CIR)
  • General form of CIR
  • Mean reversion in the CIR model
  • Term structures in the CIR model
• Disadvantage of equilibrium models
• Examples and Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Term Structure Models (Continued)

• No-arbitrage Models
• Markov vs. non-Markov Models
• The Ho and Lee Model
• The BDT Model
  • General form
  • Deriving the model from zero curve and volatility structure
• The Hull-White Model
  • A general tree-building procedure
  • Building the tree – stage one
  • Calculating branching probabilities
  • Building the tree – stage two
• The Libor Market (BGM) Model
• Using Monte Carlo Simulation with Interest Rate Models
• Examples and Exercises

Day Three

09.00 - 09.15 Recap

09.15 - 12.00 Pricing Interest Rate Options Using Term Structure Models

• Pricing Options on Zero Coupon Bonds
• Pricing Options on Coupon-Bearing Bonds
• Pricing Libor Options
  • Interest Rate Guarantees
  • Caps and Floors
  • Swaptions
  • “Cancellation Swaps“
• Pricing Structured Interest Rate Products
  • “Capped FRNs“
  • “Inverse Floaters“
  • “Fairway Bonds“
• Pricing Exotic Structures
  • Captions, floptions and other compounds
  • Ratchet caps, sticky caps, and flexi caps etc.
• Examples and Exercises

12.00 - 13.00 Lunch

13.00 - 16.00 Pricing Callable and Defaultable Bonds

• General Characteristics of Callable Bonds
• Pricing Callable Bonds
  • Single-call and multiple-call bonds
• Prepayment Models
• Integrating Prepayment Models into an Interest Rate Model
• Option-adjusted analysis
  • OAS, OAY, Option-adjusted duration, Z-Spread
• Pricing Mortgage Bonds
  • MBS, CMO, IO, PO
• Pricing Defaultable Bonds
  • Incorporating credit spreads into term structure models
• Examples and Exercises

Evaluation and Termination of the Seminar