Advanced Interest Rate Modelling (Part 1) by Pat Hagan

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