Options: an application

Earlier, we discussed the farmer wanting to protect themselves against the risk of the cocoa price falling before harvest. We suggested they could use a forward contract, or sell futures contracts.

But what if the cocoa price increased before the harvest? Do these strategies allow the farmer to take advantage of higher prices? The price in the forward contract is fixed. Marking to market in futures means the farmer receives the price they contracted to when they sold the futures contracts. However, futures offer some flexibility. The farmer could close out their position months before the delivery period by purchasing futures contracts. They would make a loss on the futures positions, but they could take advantage of further increases in cocoa prices.

Put options

Is there a strategy that would hedge against a lower price, but also allow the farmer to take advantage of an increase in price if that occurred? Yes there is: the farmer could purchase an option. We will examine the detail of options in the next steps, but here we give an idea how options provide flexible protection.

By purchasing a put option the farmer obtains the right to sell cocoa on a specified future date (for example, after their harvest) at a fixed price, known as the exercise or strike price. The seller of the put option agrees to purchase cocoa at the exercise price, if the option is exercised. To purchase the option the farmer pays the seller the option price, known as the option premium.

At harvest time, when the option expires, if the cocoa price on the spot market is below the exercise price, the farmer can exercise the put option and sell cocoa at the exercise price. The put option provides protection against the risk of a fall in the cocoa price.

If the cocoa price on the spot market is above the exercise price at harvest time, the farmer will leave the option unexercised, and sell their cocoa at the higher spot price.

Option pricing

The put option provides the farmer with protection against a fall in the cocoa price, and the cost of that protection is the option premium. What influences the option premium? At the expiry date, if the cocoa price is below the exercise price, the put option has value and will be exercised. If the cocoa price is above the exercise price, the put option has no value and will not be exercised. Therefore, to price the option we need to determine, in advance, the chances of the option being exercised.

When the farmer purchases the put option, if the current cocoa price is very much above the exercise price, there is less likelihood the option will be exercised at maturity. If the farmer purchases a put option with a short time to the expiry date, there is less opportunity for the cocoa price to fall and for the option to be exercised.

We can also examine the usual pattern of daily changes in the cocoa price. Given the time to expiry, and the current cocoa price, would the daily price changes lead to the cocoa price falling below the exercise price by harvest time? Finally, the decision to exercise the option happens in the future. To price the option now, we need to discount the future payments using a suitable discount rate.

We use these elements – time to expiry, current cocoa price, exercise price, discount rate, and the distribution of daily changes in the cocoa price – to determine the probability of the put option being exercised (or left unexercised), and from this we can price the option.

We’ll be looking at the detail of options contracts and the models used to price options in the next steps. For now, do you think purchasing a cocoa put option is a sensible strategy for the farmer?