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