16. Mathematical Models and Tools in Fixed Income Analysis

In this section

• 16.1 Bond Mathematics and Valuation Models
  • Pricing Formulas for Plain Vanilla Bonds
    Master the essential pricing formulas for plain vanilla bonds, understand the components, and learn how changing interest rates impact bond prices in this comprehensive guide.
  • Valuation of Bonds with Embedded Options
    Explore the valuation of bonds with embedded options using advanced models like the Binomial Interest Rate Tree and Monte Carlo Simulation. Understand the role of option-adjusted spread (OAS) in pricing these complex securities.
• 16.2 Interest Rate Models
  • 16.2.1 Short-Rate Models
    • Vasicek Model: Understanding the Equilibrium Short-Rate Model in Fixed Income Analysis
      Explore the Vasicek Model, an essential tool for describing interest rate evolution in bond markets. Learn about its parameters, applications, and limitations.
    • Cox-Ingersoll-Ross (CIR) Model: Understanding Interest Rate Dynamics
      Explore the Cox-Ingersoll-Ross (CIR) Model, a crucial tool in fixed income analysis, addressing interest rate volatility and bond pricing.
  • Heath-Jarrow-Morton (HJM) Framework in Fixed Income Analysis
    Explore the Heath-Jarrow-Morton (HJM) Framework, a pivotal model in fixed income analysis, focusing on its application in modeling forward rate curves and pricing interest rate derivatives.
• 16.3 Option-Adjusted Spread (OAS) Analysis
  • Option-Adjusted Spread (OAS): Mastering Bond Pricing and Investment Strategies
    Explore the complexities of Option-Adjusted Spread (OAS) in bond markets, understanding its role in pricing strategies and investment success.
  • Monte Carlo Simulation in OAS
    Explore the intricacies of Monte Carlo Simulation in Option-Adjusted Spread (OAS) analysis, a critical aspect of bond pricing and fixed income securities.
  • Practical Applications of OAS in Fixed Income Investing
    Explore the practical applications of Option-Adjusted Spread (OAS) in bond valuation and portfolio management. Learn how to use OAS to identify relative value opportunities and optimize fixed income portfolios, while understanding its limitations.
• 16.4 Duration and Convexity Calculations
  • Modified Duration for Different Bonds
    Explore the concept of modified duration for different types of bonds, including zero-coupon, fixed-rate coupon, and floating-rate notes. Learn how to calculate modified duration and its significance in managing interest rate risk.
  • Effective Convexity in Practice: Mastering Bond Pricing and Risk Management
    Learn how to compute Effective Convexity for bonds with embedded options and understand its role in estimating price changes due to interest rate movements. Compare callable and option-free bonds to optimize your investment strategies.
• 16.5 Risk Metrics and Measures
  • Value at Risk (VaR) in Fixed Income Securities
    Explore the comprehensive guide to Value at Risk (VaR) in fixed income securities, including calculation methods, applications, and limitations in bond portfolios.
  • Stress Testing and Scenario Analysis in Fixed Income Securities
    Explore the critical role of stress testing and scenario analysis in fixed income securities, focusing on risk management and regulatory compliance.