Practical implementation techniques for interest rate modelling

Led by: Dorje Brody, Reader in Mathematics, Department of Mathematics, IMPERIAL COLLEGE LONDON
Christian Fries, Head of Model Development , Rates and Hybrids, DZ BANK

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8.30 Registration and coffee

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9.00 Interest rate theory: Past practice and future direction
Overview of interest rate theory

• Short rate models, HJM framework, market models
• Pricing kernel approach, model calibration and derivatives pricing

Dorje Brody, Reader in Mathematics, Department of Mathematics, IMPERIAL COLLEGE LONDON

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10.00 Macroeconomic considerations for interest rate term structure

• Liquidity effect vs Fisher effect
• Discount bond and survival function
• New pricing formula for discount bonds

Dorje Brody, Reader in Mathematics, Department of Mathematics, IMPERIAL COLLEGE LONDON

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11.00 Morning break

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11.30 Information-based approach to interest rate modelling

• Rationale for the BHM framework
• Market information concerning projected future liquidity risk
• Diagnosis of the bond volatility structure: relation to annuities
• Pricing formulae for bond options
• Practical model implementation

Dorje Brody, Reader in Mathematics, Department of Mathematics, IMPERIAL COLLEGE LONDON

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12.30 Lunch

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13.30 Markov Functional Models: From Theory to Implementation

• Introduction to the Markov Functional Model Framework
• Advantages of Functional Modelling
• Calibration of the Interest Rate Markov Functional Model
  o Calibration to Caplets
  o Calibration to Swaptions
• Generalized Markov Functional Model Framework
• Calibration to Auto Correlation Sensitive Products
  o Auto Correlation in the LIBOR Market Model
  o Auto Correlation in the Markov Functional Model
• Markov Functional Model with Joint Calibration of Caplets and Swaptions
• Markov Functional Model with Joint Calibration of Swaptions and Bermudans
• Hybrid Markov Functional Models
• Implementation

Christian Fries, Head of Model Development , Rates and Hybrids,
DZ BANK

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15.00 Afternoon Break

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15.30 Design Patterns for Derivative Pricing and Risk Management
with Application to the Monte-Carlo Implementation of LIBOR Market Models and Lattice Implementation of Markov Functional Models

• Foundations: Random Variables and Stochastic Processes
• Separation of Model and Product Pricing Code
  o Pricing and Generic Sensitivities
• Pricing Techniques
  o Path-Dependency
  o Early-Exercise
• Abstraction of Pricing Code from Numerical Schemes
  o Products Requiring a Backward Induction
  o Products Requiring a Path-Dependent Quantity
• Application
  o Monte-Carlo Implementation of LIBOR Market Models
  o Lattice Implementation of Markov Functional Models

Christian Fries, Head of Model Development , Rates and Hybrids,
DZ BANK

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17.00 End of the Seminar