Mathematical Models and Tools in Fixed Income Analysis

In this section

• Bond Mathematics and Valuation Models
  Review the core valuation formulas used for plain vanilla and option-embedded bonds.
  • Pricing Plain Vanilla Bonds
    Study the standard pricing formulas used to value conventional fixed coupon bonds.
  • Valuation of Bonds with Embedded Options
    Review how callable, putable, and other option-embedded bonds are valued.
• Interest Rate Models
  Study short-rate and term-structure models used in advanced fixed income valuation.
  • Short-Rate Models
    Review equilibrium short-rate models commonly used to describe interest rate dynamics.
    • Vasicek Model
      Understand the Vasicek short-rate model and its role in fixed income pricing.
    • Cox-Ingersoll-Ross (CIR) Model
      Review the CIR model and how it is used to model positive short-rate dynamics.
  • Heath-Jarrow-Morton (HJM) Framework
    Study the HJM framework for modeling the evolution of the full forward-rate curve.
• Option-Adjusted Spread Analysis
  Review the main concepts and tools used to estimate and interpret option-adjusted spread.
  • Option-Adjusted Spread
    Understand what option-adjusted spread measures and how it is used in bond valuation.
  • Monte Carlo Simulation in OAS Analysis
    Review how Monte Carlo simulation supports path-dependent OAS estimation.
  • Practical Applications of OAS
    Study how OAS is applied in relative value work, risk analysis, and security selection.
• Duration and Convexity Calculations
  Review advanced duration and convexity calculations used in bond risk measurement.
  • Modified Duration for Different Bonds
    Study how modified duration is calculated and interpreted across different bond structures.
  • Effective Convexity in Practice
    Review how effective convexity is estimated and applied to bonds with embedded options.
• Risk Metrics and Measures
  Study quantitative risk measures used to monitor fixed income portfolios and stress exposures.
  • Value at Risk (VaR) in Fixed Income
    Understand how VaR is estimated and interpreted in fixed income portfolio risk management.
  • Stress Testing and Scenario Analysis in Fixed Income
    Review how stress tests and scenarios are used to assess fixed income portfolio resilience.