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Interest Rate Modelling for the New Era by Pat Hagan: Head of Quantitative Analytics, Chief Investment Office, JP Morgan |  |
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09.00 – 10.30: Managing Smile Risks
- Basics: discount factors, FRAs, swaps, and other delta products
- Curve stripping, bucket deltas, and managing IR risks
- Martingales & the fundamental theorem
- Vanilla options (caps, floors, and swaptions) & martinga
- 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
- Levy based models for managing volatility surfaces
10.30 - 10.45 Break
10.45 – 12.30: Intermission: Market technicals
- Money vs. scrip
- Holiday calendars, business day rules, and schedule generation
- Day count fractions
- Ref rates & basis spreads
- Leverage, cost of funds, and the credit crisis
Managing exotic risks
- 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
- Summary
12.30 - 13.30 Lunch
13.30 – 15.15: Practical pricing of exotics
- LGM model
- Callable swaps (Bermudans)
- Calibration strategies and the selection of calibration instruments
- Connection between calibration instruments and vega risks
- Explicit calibrations for Bermudan
- Predicted vs. actual vol matrices for different calibrations
- Dependence of Bermudan price on choice of calibration instruments
- Dependence of hedges on calibration choices
- Conclusions
15.15 - 15.30 Break
15.30 – 17.15: Adjusters and risk migration
- Mis-hedging, mis-pricing, and the need for risk migrators
- Price sharpening via adjusters
- Example: Correcting a Bermudan calibrated to ATM swaptions
- Example: Correcting a Bermudan calibrated to caplets
Pricing/hedging callable range notes & accrual swaps
- Definition of the deal
- Mismatched payoffs & convexity corrections
- Using replication to price non-callable range notes
- LGM model and potential calibration strategies
- Potential mishedging of swaption or caplet risks
- Using internal adjusters to correct prices and hedges