Commodity solutions are often structured using correlation-dependent options. Let’s say a car producer wishes to hedge their copper and aluminium costs using a single option.
They enter into a 3-month equally weighted basket option. With the 3 month prices of CU and AL being $9,000 and $2,500 respectively, the strike price of an ATM basket call option would be $5,750 (($9,000 + $2,500) / 2).
What would be the payoff on this option? Since it is equally weighted the option will payout at maturity if the average of the two prices is above the strike. So if by maturity CU goes to $10,000 and AL to $3,000 then the basket value is $6,500. The option would pay out $750 ($6,500 – $5,750).
How much would this cost?
First things first – how much would ‘vanilla’ call options on the individual metals cost? If we use an implied volatility of 25% for both options, we have:
3M ATM AL option: $128 / tonne
3M ATM CU option: $459 / tonne
For a total of $587 / tonne.
We can use the same parameters for a basket option, but the model requires an input for the price correlation between the two metals. In part I we showed that the payout would depend on whether or not the metals moved in the same direction or not. A recent research piece by the LME suggested that the correlation between the two metals was 0.56. This returns a basket price of $271.58.
A theoretical negative correlation of -1 returns a premium of $169.73 while +1 generates a premium of $293.45. This means the basket call option is ‘correlation positive’. For this second scenario the premium is equal to 50% of a vanilla CU call + 50% of a vanilla AL call. This correlation values implies that the metal prices will always move in the same direction. If this is upward, the payout on the basket will be maximised.
Instinctively, a user would see the basket option as being ‘cheaper’ and so may decide it is better value. Perhaps, but perhaps not.
Earlier in the post we showed that if the 3 month prices of CU and AL being $9,000 and $2,500 respectively, the strike price of an ATM basket call option would be $5,750 (($9,000 + $2,500) / 2).
What would be the payoff on the basket vs. the individual options if the prices of the metals at expiry were $9,500 and $3,000?
The basket option would pay out [($9,500 + $3,000) / 2] – $5,750 = $500
Since the price of both metals has increased beyond the strike the vanilla call options would pay out $500 each, so $1,000 in total.
The basket option has a lower premium but a lower payout – it is not necessarily cheap but is relatively inexpensive. It pays out 50% of the vanilla options as the basket is equally weighted. Don’t forget that cheapness refers to the idea that an option is undervalued relative to some notion of fair price.