# Derivatives on commodities

## Pricing and use of derivatives on commodities

- 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

## 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

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 :*

- Marchés financiers des matières premières (Catalogue Finance)