Contents

• List of Figures
• List of Tables
• Outline
  • About this document
  • The course
  
  
• Introduction
  • What is a derivative?
  • A short history lesson
  • Why derivatives?
  • The forward contract
  • The futures contract
  • Options
  • The market participants
  • MMA: Option strategies
  
  
• Hedging with Futures
  • Specifications
  • Margins
  • Open interest and volume of trading
  • Future-spot convergence
  • Hedging with futures
  • Optimal hedge ratio
  • Rolling the hedge
  • MMA: A simulation example of the basis, the basis risk and the mark-to-market procedure
  
  
• Futures and Forwards
  • Compounding issues
  • Short selling
  • The forward price
  • Coupons, Dividends and FX forwards
  • Forwards vs futures
  • Stock index futures
  • Hedging using index futures
  • Cost of carry
  • Futures prices and future spot prices
  • Appendix: Hedging with BLOOMBERG
  • Appendix: Futures prices and arbitrage opportunities
  
  
• Valuing Cash Flows
  • State prices
  • The pricing kernel
  • The risk-neutral probability measure
  • The 50-50 rule
  • Multiple states and assets
  
  
• Modelling: Discrete state space and time
  • State-space and time
  • Models for the short rate
    • The Ho and Lee tree approach
    • Choosing the parameters
    • Claim pricing
    • Other models
    • The binomial framework of Cox, Ross and Rubinstein
  • MMA: Extraction of the binomial tree parameters
  
  
• Modelling: Continuous state space -- discrete time
  • The building blocks
  • Brownian motion in discrete time
  • The market
  • Risk neutral pricing and arbitrage
  • The Black-Scholes formula
  • An alternative approach
  • Other models
  • MMA: Programming a GARCH-type estimation
  • MMA: Pricing options with the Heston and Nandi GARCH-type model
  
  
• Modelling: Continuous state space and time
  • Brownian motion in continuous time
  • Itô's formula
  • The geometric Brownian motion
  • The Black-Scholes formula I
  • Girsanov's theorem and the risk neutral measure
  • The Black-Scholes formula II
  • The martingale representation theorem
  • The Black-Scholes formula III
  • Implied volatilities
  • Stylized facts
  • Extensions to the BS methodology
  
  
• The Greeks
  • Naked, Covered and Stop-Loss strategies
  • Delta
  • Theta
  • Gamma
  • Vega
  • Rho
  • Dividends and FX options
  • Portfolio insurance
  • MMA: The derivation and payoffs of the Greeks
  • MMA: Option strategies and the Greeks
  • MMA: Dynamic delta hedging
  • MMA: The convergence of the dynamic delta hedging towards the option price
  
  
• Value at risk
  • MMA: Principal component analysis of the yield curve
  
  
• About this document ...