Module 5: Fixed Income

Fixed Income Products and Analysis

  • Names and properties of the basic and most important fixed-income products
  • Features commonly found in fixed-income products
  • Simple ways to analyze the market value of the instruments: yield, duration and convexity
  • How to construct yield curves and forward rates
  • Swaps
  • The relationship between swaps and zero-coupon bonds

Stochastic Interest Rate Modeling

  • Stochastic models for interest rates
  • How to derive the pricing equation for many fixed-income products
  • The structure of many popular one-factor interest rate models
  • The theoretical framework for multi-factor interest rate modeling
  • Popular two-factor models

Calibration and Data Analysis

  • How to choose time-dependent parameters in one-factor models so that
  • Today’s yield curve is an output of the model
  • The advantages and disadvantages of yield curve fitting
  • How to analyze short-term interest rates to determine the best model for the volatility and the real drift
  • How to analyze the slope of the yield curve to get information about the market price of risk

Probabilistic methods for interest rates

  • The pricing of interest rate products in a probabilistic setting
  • The equivalent martingale measures
  • The fundamental asset pricing formula for bonds
  • Application for popular interest rates models
  • The dynamics of bond prices
  • The forward measure
  • The fundamental asset pricing formula for derivatives on bonds

Heath Jarrow and Morton Model

  • The Heath, Jarrow & Morton (HJM) forward rate model
  • The relationship between HJM and spot rate models
  • The advantages and disadvantages of the HJM approach
  • How to decompose the random movements of the forward rate curve into its principal components

The Libor Market Model

  • The Libor Market model
  • The market view of the yield curve
  • Yield curve discretisation
  • Standard Libor market model dynamics
  • Numéraire and measure
  • The drift
  • Factor reduction

Further Monte Carlo

  • The connection to statistics
  • The basic Monte Carlo algorithm, standard error and uniform variates
  • Non-uniform variates, efficiency ratio and yield
  • Co-dependence in multiple dimensions
  • Wiener path construction; Poisson path construction
  • Numerical integration for solving SDEs
  • Variance reduction techniques
  • Sensitivity calculations
  • Weighted Monte Carlo

Multiple Curve Interest Rate Modeling

  • LIBOR curve data and post-LIBOR world
  • Multi-curve stripping to match swaps
  • OIS discount & risk-free benchmarks
  • Tenor basis & tenor volatility
  • Optionality in fixed income products
  • Industry uses of LMM, HJM, G2++

Fixed Income Market Practices

  • Basics: discount factors, FRAs, swaps, and other delta products
  • Basic curve stripping, bucket deltas, and managing IR risks
  • Interpolation methods
  • Risk bleeding
  • Scenarios-based risks and hedging (wave method)
  • Current Market Practices
  • Advanced stripping

Volatility Smiles and the SABR Model

  • Vanilla options: European swaptions, caps, and floors
  • Arbitrage Free SABR
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