# Compound Options

Did you know you could buy an option on an option contract? While it sounds like you could be subjecting yourself to some pretty crazy leverage, the intended use is actually to reserve the right to purchase an option at a later date, rather than to apply hideous amounts of leverage. Further, compound options are, as far as I know, strictly an OTC (over the counter) security (I have never come across a compound option on an exchange, but I have never really looked, to be fair).

Let’s say someone want to purchase shares of ABC in 1 year from now (because they do not have the money to make the purchase right now, but expect a large sale to complete in 1 year, thus providing them with the cash to actually buy the shares). If they wanted to protect themselves from a rise in the price of ABC before they can buy it, they could purchase an option on ABC – for example a 1 year call option with a strike price of \$50/share (perhaps ABC is trading today for \$40). This option might be \$2/share. Let’s further assume the company wants to buy 1 million shares.

But what if they don’t have enough money right now to even purchase the option? Afterall, while purchasing 1 million shares of ABC at \$50/share would cost \$50 million, just purchasing the option to buy it at \$50 for the next 1 year would cost \$2 million. In this case, they could buy an option on the option to limit the maximum purchase price they will pay.

This ‘compound option’ could need to be a 6 month call option with a strike price of \$2.00 on the 1 year ABC \$50 call option. (I know, it’s very confusing if you are not already familiar with options.) The compound option cost varies a lot depending on the volatility of ABC (more volatile = more expensive) If ABC was not very volatile at all the compound option might cost \$0.08/share. The total cash outlay would be only \$80,000 to basically secure the ability to purchase 1 million shares of ABC for no more \$50/share for the next year (actually \$52,080,000 after factoring costs of the options contracts).

NOTE: As Michael James points out, if the volatility of ABC was higher (20% versus 10%) the price of this compound option might be dramatically higher at about \$1.10/share! See the comments section below for more information.

Now, if you recall, OTC options are not normally very liquid as the counterparties are dealing directly with eachother in a tailored agreement. So even if ABC started to trade at \$60, meaning the compound options you bought for \$80,000 are now worth over \$10 million, you might be hard pressed to find a buyer for a compound option. You would more than likely have to exercise your compound option to purchase the regular option and then exercise THAT option to purchase ABC for \$50 million and then sell it in the market for \$60 million.

Incidentally, your net gain would be calculated as \$60 million less the purchase price of \$50 million, less the regular option purchase price of \$2 million, less the \$80,000 to purchase the compound option. This is a total gain of \$7.92 million.

If ABC was trading below \$50/share, you would just let the compound option expire worthless, you would not have spent the \$2 million on the regular option, and you could just buy ABC on the open market.

Thanks to Michael James on Money for his help on this post.

Preet Banerjee
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• Michael James

I don’t understand how the example you give could happen in the real world. If the option at \$50 has a premium of \$2, it seems to me that the premium of the compound option should be about \$1.50 rather than \$0.08. Otherwise, compound option writers would be losing a lot of money.

• Preet

@Michael James – option writers never lose money on paper unless their positions are naked and they are forced to cover their positions at unfavourable prices. The compound option buyer may let the compound option expire worthless, in which case they are out their money and the compound option writer pockets the premium. If the compound option buyer exercises their option to buy the \$50 call options on ABC, then they must further pay \$2/share to the compound option writer in exchange for taking over those options (which themselves may expire worthless or not).

In the hypothetical example in the post, if the regular option is trading at over \$2.00, the compound option is in-the-money. If the regular option’s price is below \$2.00, the compound option which has a strike price of \$2.00 is out-of-the-money.

Does that makes sense? By all means, let me know if I’ve missed something…

• Michael James

Hi Preet,

I understand the logic that makes the compound option premium lower than the option premium, but I don’t see why it would be very much lower. Continuing with your example, suppose that the stock rises to \$55. The odds are against this, but not heavily so (maybe 20%?). The option buyer pays \$2 and gets back \$5 for a 150% return. This is a fair return given the moderately low probability outcome. However, the compound option buyer invested only \$0.08 and ultimately gets back \$5-\$2=\$3 for a whopping 3650% return. This is why I was guessing that the premium of the compound option ought to be in the \$1.00 to \$1.75 range.

• Preet

Okay, I think I see the disconnect – the compound option buyer actually pays \$2.08, not \$0.08, to get that \$5. (There may not be a market for the compound option since it is tailored to the two parties.) They are actually worse off if they used a compound option and ABC ends up in-the-money. They are basically paying \$80,000 for the option of more time to decide if they will buy the regular option for \$2 million.

If ABC ends up out-of-the-money (and their respective option expires worthless) they are only \$80,000 out of pocket with the compound option versus \$2 million out of pocket with the regular call option.

What I should’ve done is use a compound option with an expiry date that slightly overlaps the beginning of the regular call option to make the example more clear. i.e. if the regular call option was out of the money at expiry of the compound option but still had time value over \$2.00, then the compound option could be in the money even though the regular option is not.

In fact, compound options generally have two different expiry dates and strike prices. Sorry for the confusion – and please do let me know I’m not addressing your question properly (or if I’m wrong!) :)

• Michael James

Instead of paying \$2.08 to get a chance at \$5, I think of it as paying \$0.08 for a chance at \$3 (because I don’t pay the \$2 until I’m sure that I will get the \$5). This is an enormous return that the compound option writer is crazy to pay, assuming that I understand you correctly. Your explanation seems consistent with my belief that the compound option premium should be much higher than \$0.08.

• Preet

“…that the compound option writer is crazy to pay…” – the writer supplies the contract in return for payment – so they do not pay, they collect income. Can you restate that – I don’t think I’m clear on what you meant.

I asked a colleague for a calculation on pricing to get an idea of what the theoretical actual pricing would look like:

For something like the above scenario, an implied volatility of 10% would yield a compound option price of \$0.075 and 20% would yield \$1.10. So the pricing is very sensitive to implied volatility of the underlying asset – and quite frankly 20% is more likely than 10% so I’ll ammend the post and thanks for keeping me honest! ;)

• Preet

@Michael James – I’ve amended the post to reflect the higher price with higher (and more appropriate) volatility assumptions. Thanks! I appreciate your contributions very much!

• Michael James

Hi Preet,

What I meant was that for the case where the stock goes up to \$55, the compound option writer will have to supply an option struck at \$50 which will cost (at least) \$5 at this point. So, the compound option writer was taking a chance on having to pay \$5 in return for \$2 now plus the initial premium. A compound option premium of \$1.10 seems like it is more in the ballpark to compensate for the risk.

• Preet

Oh okay – most compound option writers will already own the option (covered write) so their cost is fixed. They would write the compound option for a higher strike price than the premium they paid thereby getting the income from the write, and if it gets called away, ensuring it is sold from them at a higher price than they bought it. I suppose writing naked compound options could happen, but if due dilligence was done, since the two counterparties deal direct – I doubt the deal would be entered into. Unless your a french rogue trader?… :)