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Advanced Interest Rate Modelling (Part 1)

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Advanced Interest Rate Modelling (Part 1)

Course Running Time: 4 Hours 30 Minutes


Course Outline:

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)

About the Presenter:

Pat Hagan: Consultant & Mathematics Institute, Oxford University

Pat Hagan received his BS and Phd from the California Institute of Technology, where he graduated at the top of his class. Before entering banking, he designed chemical reactors for Exxon and did physics research at Los Alamos. He specializes in designing trading systems, as well as developing the component models, calibration methods, and numerical algorithms. He has created several industry standard models and methodologies, including the SABR and LGM models, autocalibration, and adjustors.

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