**Advanced Interest Rate Modelling (Part 1)**

**Presenter: Pat Hagan: Consultant & Mathematics Institute, Oxford University**

**Video Lectures**

**Basic Fixed Income Instruments: (Running Time: 44:30)**

**Current Market Practice (Running Time: 1:44:00)**

**Advanced delta: (Running Time: 1:04:32)**

**Arbitrage Free SABR (Running Time: 56:26)**

Basic Fixed Income Instruments

- Basics: discount factors, FRAs, swaps, and other delta products
- Basic curve stripping, bucket deltas, and managing IR risks
- Martingales & the fundamental theorem
- Vanilla options (caps, floors, and swaptions) & Black's model
- Vol matrices, bucket vegas, and managing vol risks
- Smiles, local volatility models, and equivalent volatilities
- Mishedging, and the development of the stochastic vol model
- Using the SABR model to manage volatility smiles, hedging stability
- Lévy based models for managing volatility surfaces

Current Market Practice

- Money vs. scrip
- Holiday calendars, business day rules, and schedule generation
- Day count fractions

Advanced delta

- Reference rates & basis spreads
- Stripping reference rates to obtain basis spreads
- OIS discounting and dual-curve stripping
- Cross-currency basis curve; collateralizing legs in alternate ccy
- Leverage, cost of funds, and the credit crisis
- Moving to scenario-based risks and hedging

Arbitrage Free SABR

- Arbitrage in the SABR model
- Reduction to the effective forward equation
- Arbitrage free boundary conditions
- Exactly conservative numerical methods
- Comparison with historical data
- Hedging under SABR model
- Closed-form solutions; boundary layer analysis