Module 4: Fixed Income & Commodities

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

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

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

Mathematica for Quantitative Finance

  • The Principles of Mathematica
  • Financial Statistics: Financial Data; Descriptive Statistics, Distributions; Probabilities; Multiple Datasets
  • Quantitative Methods for Finance
  • Using Calculus and Linear Algebra in Quantitative Finance

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

Energy Markets and Derivatives

  • What's hot in the energy industry
  • Shale. Fracking
  • Spot electricity markets: unique characteristics and prices
  • North American Electric Reliability Corporation (NERC)
  • Stochastic processes to model electricity spot prices
  • Physical Forward and Futures Markets
  • Contango and backwardation
  • Balancing and reserve market

Energy Derivatives Trading and Risk Management

  • Participants' risk exposure in electricity markets
  • Price volatility
  • Fluctuation of electricity production costs
  • Hedging with electricity futures for generators, marketers and end-users
  • Risks of hedging with electricity futures
  • "Stack and Roll" hedging for the long-term periods
  • "Hedging with electricity options and crack spreads
  • Speculation (views taking) using electricity futures
  • Politics of Speculation. Dodd-Frank Act
  • Restrictions to oil speculation and high frequency commodity trading
  • Energy trading case study. Sparks spread
Lecture order and content may occasionally change due to circumstances beyond our control; however this will never affect the quality of the program.