Financial Market Mathematics 3: Interest Rate Models

Valuation and necessity of Interest Rate Models
  • Valuation
  • No-arbitrage principle
  • Yield curve deformation analysis
  • Interpolation methods
Option pricing
  • Limits of the Black & Scholes model applied to interest rate options
  • Pricing of swaptions
  • Pricing of digital and Bermudan options
  • Practical workshop
  • Pricing in EXCEL™ of swaptions, digital and Bermudan options
  • Model calibration
  • Differences between the normal and log-normal models
  • Volatility smile: SABR model
  • Parameter calibration in SABR
  • Portfolio management: second derivatives
  • Volga-negative management
Various implementation tools: strengths and weaknesses
  • Analytical methods
  • Trees
  • Monte Carlo method
  • Choice of methods
  • Practical workshop
  • Apply the Monte Carlo method in EXCEL™
History of interest rate models: description and application
  • Model of Vasicek and Cox-Ingersoll-Roll
  • Model of Black-Derman-Toy
Hull & White Model
  • Description
  • Practical workshop
  • Construct the model in EXCEL™ VBA
  • Application to swaptions
  • Model calibration and limits
Market Model: Brace - Gatarek - Musiela (Libor market model)
  • Description
  • Market model/theory
  • Model calibration and limits
Winning formulas and changes in probabilities: Girsanov theorem
  • Change of measures in a stochastic process
  • Risk neutral probabilities/forward neutral
Extensions
  • Pricing of a CMS option: calibration of the convexity spread
  • Pricing of an option on CMS spread with the BGM model

  • Valuation by arbitrage
  • Master interest rate models and their implementation
  • Assess the limitations of valuation models
  • Master the valuation of options using spreads
  • Comprehensive coverage of the application and limitations of interest rate models
  • Front, middle and back office
  • Risk management
  • Audit
  • Fund managers
  • ALM managers
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