Advanced Interest Rate Modelling (Part 2) by Pat Hagan

Advanced Interest Rate Modelling (Part 2) by Pat Hagan

Presenter: Pat Hagan: Consultant & Mathematics Institute, Oxford University
Video Lectures:

Managing Exotics:  (Running Time: 1.01:14)

Practical Pricing of Exotics & Adjustors and risk migration: (Running Time: 1.24:07)

Pricing callable range notes (accrual options): (Running Time: 53:54)

Managing Exotics

  • Three elements to modern pricing: model, calibration, and evaluation
  • Choosing a model and the five main interest rate risks
  • HJM models - strengths, weaknesses, usage
  • BGM/LMM models - strengths, weaknesses, usage
  • Short rate models - strengths, weaknesses, usage
  • Markovian models - strengths, weaknesses, usage

Practical Pricing of Exotics

  • LGM model
  • Closed form zero coupon bond and swaption prices under the LGM model
  • Callable swaps (Bermudans)
  • Calibration strategies and the selection of calibration instruments
  • Forward volatility risk
  • How the risks, hedges, and values of the exotic depend on the calibration instruments

Adjustors and risk migration

  • Classic mis-hedging problem
  • Risk migration and the adjusted price
  • The adjusted price
  • Examples

Pricing callable range notes (accrual options)

  • Standard range note
  • Using replication to price the non-callable range notes. Convexity adjustments
  • Pricing requirements
  • Libor market model vs. external adjustors vs. internal adjustors
  • Using internal adjustors with the LGM modle
  • Pricing, risk analysis, and hedging the embedded and external options
  • General procedure for callables with embedded options