CMS and CMS spread options

CMS analysis and risk management

Course objectives

  • Master the evaluation techniques of CMS spread options

  • Master the CMS convexity adjustments

  • Analyse the risk of CMS and CMS spread options

CMS convexity adjustment

  • Why is the convexity adjustment needed?
    • The basic formula
    • Limitation
  • Smile replication method
    • SABR volatility smile
    • Replication method
  • Replication model limitation
    • Adjustments for far out of the money strikes
    • Swap settlement swaptions

Spread options

  • Black-Scholes formula for spread options
    • Normal rates
    • Log-normal rates
    • Smile impact on option prices
  • Use historical volatility or historical correlation?
  • Use implied correlation or historical correlation?
    • Implied correlation calculus
    • Historical correlation risk management limitation
    • Implied correlation risk management limitation
  • Digital spread options
  • Volatility smile
    • Copula method
    • Volatility smile impact

CMS spread exotic options

  • Different types of CMS spread exotic options
  • Evaluation models
  • Calibrate on which options

CMS spread risk management

  • Why do not standard risk management tools work?
  • Cross-gamma risk management

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