**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