Derivatives on commodities

Pricing and use of derivatives on commodities

Course objectives

  • Understand the functioning of key derivatives on commodities
  • Identify all necessary market data required for pricing of commodities derivatives
  • Understand financial models adapted to commodities, as well as the main valuation techniques
Course content

Derivatives on commodities

  • Standard Futures :
    • Future Contract / Forward Contract
    • Option on a futures contract

Case Study: Mechanics of a future contract on Brent IPE

  • Swaps:
    • Standard swap / currency swap
    • Asian swap

Case Study: Mechanics of an Asian swap on Zinc LME

  • Options:
    • Asian option / Exchange option
    • Spread option
    • Forward start option
    • Swaption
    • Swing / take-or-pay option
    • Real option

Case Study: Mechanics of a spark spread option

Market data required for pricing

  • Curves of commodities:
    • Spot / Forward / Future
    • Contract for differences
    • Swap
    • Interpolation and extrapolation: linear and backstep
  • Volatility curves:
    • Smile
    • Vanilla / forward volatility
    • Swaption volatility
    • Variance interpolation: linear and backstep
  • Correlation matrix:
    • Intra-underlying correlation
    • Inter-underlying correlation
    • Correlation curve
  • Currency and exchange Curves:
    • Zero-Coupon
    • Discount factor
    • Interpolation of discount factors
    • Forward exchange
    • Swap point
    • Foreign Exchange volatility

Modeling and pricing methods

  • Financial models:
    • Spot Model / Forward Model
    • Black & Scholes Model
    • Mean reversion
    • Diffusion in a forward with risk neutral probability
  • Analytical formulas:
    • Black formula for pricing a European option on forward contract
    • Calculation of Greeks
  • Equivalent lognormal process :
    • Closed formula for the pricing of an Asian option on the arithmetic mean of a forward contract
    • Calculation of Greeks
  • Numerical methods:
    • Pricing by trees
    • Pricing by EDP
    • Pricing by Monte Carlo simulations

Pricing commodities derivatives

Case Studies:

- Pricing a forward contract on NYMEX natural gas

- Pricing a currency swap OTC on Aluminium LME

- Pricing of a European option on future IPE Brent

- Pricing an Asian option on WTI NYMEX crude future




Léopold Tsogo

Léopold Tsogo

PhD in Applied Mathematics from the University of Technology of Compiègne, Léopold began his career as a teacher-researcher in modeling complex systems. He then worked as a financial engineer, first within an edition in financial software, and now in investment banks on interest rate derivatives, commodity derivatives and equity structured products.

Léopold Tsogo also teaches :



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