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Compound Options

Key facts
A compound option is an option to buy or sell another option.
There are relatively few uses for single vanilla compound options.
They can be used as a hedge for contingent exposures, such as the interest rate and foreign exchange risks that will be incurred if a company wins a tender contract but that will not exist if the company loses.
They can also be used as a highly-leveraged way to gain exposure to the underlying while limiting downside to the small initial premium.
However, in strips, or in combination with other options, compound options can be used to create less specific and more useful products, notably pay-as-you-go options.
These give holders tailored and cancellable exposure to their chosen underlying asset.
They resemble some forms of contingent premium options but are created and behave very differently.

Caption
Name sometimes given to an option on an interest rate cap. The option on a floor is sometimes known as a floortion.

Chooser option
An option that is neither a call nor put until, at a predetermined date known as the choose or choice date, or at any time during a preset chooser period, the holder of the chooser may trade it in for either a call or put option. If the call and put have identical strikes and expiry dates the option is called a standard chooser or regular chooser and can be priced via an analytical model. If they differ in strike or expiry they are called complex choosers and can only be priced using numerical models. Choosers can be European-style or American-style in the sense that the holder is either given the choice of a European put or call or an American put or call. A chooser is not strictly speaking a compound option as in its basic variety the holder pays no exercise premium for choosing call or put and cannot simply let the choice expire. It is more similar to a European-style straddle (simultaneous purchase of a put and call) but, since the holder must choose between one or the other at some point, it is cheaper. It suits aggressive investors who wish to take a view on volatility. The pricing relies on put call parity and the fact that the option writer knows that the option holder will always choose the more valuable option on the choose date. So, if the call is more valuable, the holder of the chooser will choose it, exercise it and create a synthetic put by shorting the underlying and rolling the position forward at the strike price. Also known as a double option, dual option or preference option.

Compound option
The right to buy or sell for a pre-agreed amount at a set future date a second option of predetermined specification. This second option is known as the underlying option or back option and the option to buy or sell the underlying options is known as the front option. The compound option purchaser pays an initial premium (the front premium) and if they choose to exercise the right to buy the underlying option they pay an exercise premium (the back premium). The sum of these two premiums is greater than the premium that would have had to have been paid for the underlying option at the outset. The higher the initial premium, the lower the exercise premium and vice versa. A higher initial premium also results in a lower total premium. Compound options can be used to lock in the forward volatility curve but are most often used to hedge contingent exposures such as tender contracts.

Pay-as-you-go option
An option whose premium is payable in instalments at the beginning of each period at the discretion of the holder. At each period start the purchaser can elect not to make a payment, in which case the option is terminated. The initial upfront premium for the pay-as-you-go option is below that for a conventional option but pay-as-you-go options are more expensive than conventional options if all the premiums are paid. In this structure, the holder is long a strip of compound options whose maturity matches the tenor of the payment periods. Also known as an instalment option, though this is more usually applied to a type of contingent premium option, instalment option. Also occasionally known as a rental option (since if the holder misses a payment, the option is 'repossessed'), mini-premium option and step payment option.
Example
A company might have sold a three-year floating-rate note that the buyer can put back under certain circumstances. In return for this embedded option, the company receives a significant discount on its coupon payments. The company is not very happy with the interest rate outlook and thus wants to hedge this floating rate exposure. A normal three-year quarterly cap with a 7.35% strike would cost 174 bp. However, should the loan be called, the interest rate hedge will no longer be required. They therefore decide to enter a pay-as-you-go (or instalment) cap which would cost 23 bp per period (the rental payment). The company can simply terminate the cap when desired by ceasing to make instalment payments. This scenario can be of use when the underlying note gets called, or when the company decides it no longer requires the protection of the cap. The price of the option will depend on the termination date of the option and so the number of instalment payments made. If used for the whole original maturity it will be more expensive than a vanilla option.

Wish collar
A risk reversal in which one of the two parties has the right to change the notional amount of one side of the trade at a future date and time.


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