Pricing FCPO options with Black-76

Options on crude palm oil futures give the right, but not the obligation, to buy (a call) or sell (a put) an FCPO futures contract at a fixed strike. Pricing them is straightforward once you use the right version of the model.

Why not plain Black-Scholes?

Black-Scholes prices options on a stock you have to pay for today. Holding the stock instead of cash costs interest, and that cost of carry is built into the formula. A futures contract costs nothing to enter: you post margin, not the full price. Fischer Black's 1976 version removes the carry and works directly with the futures price F:

The only role left for the interest rate r is discounting the payoff. That is why FCPO option prices barely move when rates change.

The Greeks for a palm oil position

• Delta is the change in the option price per RM1 move in the futures. A delta of 0.45 on a 25-tonne contract behaves like about 11 tonnes of futures. It is the hedge ratio.
• Gamma is how fast delta changes. It is highest near the strike and close to expiry, which is why short-dated at-the-money options move so sharply.
• Theta is the value lost each day. Option buyers pay theta and sellers collect it. It speeds up in the last few weeks.
• Vega is the price change per volatility point. Palm oil volatility jumps around MPOB report days and El Niño headlines, and vega is your exposure to that.
• Rho is tiny for futures options, about −T × price, because rates only affect discounting.

Implied volatility tells you what the market expects

Every input to Black-76 is observable except volatility. If you take the option's market price and solve the formula backwards for σ, you get the implied volatility. This is the market's price for uncertainty.

• If implied volatility is above what you expect palm oil to realise, options look expensive, which favours selling premium.
• If it is below, options look cheap, which favours buying protection before an MPOB report or a policy decision.

There is no closed-form inverse, so you solve it numerically. A simple bisection between 0.01% and 500% converges in a few dozen steps.

Limits of the model

• It assumes one constant volatility. In reality out-of-the-money options trade at different volatilities (the skew).
• It assumes European exercise, only at expiry. American-style options can be worth slightly more.
• Liquidity in FCPO options is thinner than in futures, so quoted prices can sit away from the model.

For education only. Not trading advice.