Online Finance – Exotic derivative products – Compound options

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.

Definitions

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.

Contingent premium options

Key facts

One important difference between options and other derivative instruments such as forwards and swaps is that, generally speaking, the buyer of an option has to pay an upfront premium to purchase protection or express an investment view. This cash outlay is not always convenient and so structures have been designed that defer premium payments so removing the need to make an upfront payment. In the same way that some options’ strike price is only set on expiry, to more exactly match the holder’s risk profile or investment views, the premium payment for these contingent premium options is dependent on the final level of the underlying. In general, the structure ensures that holders pay for options they use and do not pay for options that turn out to have been unnecessary.

Contingent premium options are constructed from a combination of standard options and digital options and are usually more expensive than vanilla options that offer the same level of protection. The simplest varieties combine the purchase of a vanilla option with the simultaneous sale of a digital option. The incorporation of a digital option makes a very wide variety of structures possible. If the digital option is struck on the same underlying as the vanilla option component of the contingent premium option, then the option is known as a regular contingent premium option. If it is not, it is called a cross-contingent premium option. The digital option can be European-style/at-the-money or American-style/one-touch. Its strike price conditions can vary in as many ways as a naked digital. Strips of digital options can be sold to create instalment-like premium payments. Because of this, contingent premium options are sometimes known as instalment options, and so confused with pay-as-you-go options when the latter are referred to by the same alternative name. The crucial distinction between contingent premium options and pay-as-you-go options is that in the former, because of the embedded digital option(s), the payment or non-payment of the premium is dictated entirely by the behaviour of the underlying. Because the latter are compound options, the holder has ultimate control over the payment of the premium.

Definitions

Contingent premium option

A path-dependent option for which no upfront premium is payable. In one simple version the premium is paid at expiration but only if the option expires in-the-money. Even if the option is in-the-money, but not deeply enough to recoup the premium, the option still has to be exercised and the premium paid. If the option expires at-the-money or out-of-the money, no premium is paid. For the option holder to benefit, the option either has to expire at- or out-of-the-money or it has to expire sufficiently deep in-the-money to recoup the contingent premium. The premium is more expensive than a conventional option premium because it is paid only if the option expires in-the-money, and this is not guaranteed. The premium can be approximated by dividing a conventional premium by the probability of the option expiring in-the-money, i.e. its delta adjusted for the time value of money. Also known as the paylater option.

Contingent premium options are constructed from the purchase of a vanilla option and the simultaneous sale of a digital option. In the simplest case this digital option is struck at the same level as the vanilla option strike with a payout equal to the premium the provider of the contingent premium option calculates as sufficient compensation for the sale of the vanilla option. If the vanilla option moves into the money, so does the digital creating the premium payment. If the option remains out-of-the-money, so does the digital so no premium is payable. Contingency can be applied to any derivative. So a contingent cap is a cap whose buyer pays a small upfront premium and then has to pay a further premium instalment if the selected index fixes above the preset contingency level. If the contingency level is never reached, then the premium is lower than for a conventional cap. If the contingency level is breached then the total premium payable is higher. In more tailored versions of the structure the premium is calculated and potentially paid several times during the life of the option, not just at maturity. Structures that incorporate multiple digital options, give this type of contingent premium options their other name, instalment options (see over).

Cross-contingent premium option

A contingent premium option on one asset whose premium is contingent upon movements in another.

Deferred premium option

A standard option except that the premium is payable at expiry rather than upfront. More expensive than a conventional option by an amount equal to the cost of having effectively borrowed the premium from the option provider. This is not a true contingent premium option because the premium is payable regardless of the level of the underlying. It is the combination of a conventional option and a loan.

Instalment option

An option with zero upfront premium for which the buyer pays a pre-specified amount if the underlying trades through one or more pre-determined levels at any time over the life of the option. If the underlying fails to trade through any of these instalment levels, the buyer will have acquired the option at no cost. See example 1.

The instalment structure can be applied to a most basic options and is behind many, seemingly separate products. For example the self-funding cap has no up-front premium. Instead, a predetermined premium is paid only at those strike resets where the cap is in-the-money. If the cap expires out-of-the-money, the buyer makes no payment. In exchange for the guarantee that its premium will not be wasted, the premium is higher than for a conventional cap.

Depending on the type of digital option sold, the structure can be altered so that the premium from the sale of the embedded digital options is used to create not an all-or-nothing premium payment but a high/low premium choice. In the reflex cap the premium is paid periodically, and each instalment is dependent upon a trigger rate being reached. The total premium will be low if the reference rate stays below the trigger, but will higher if the rate is above that trigger. See example 2.

Sometimes the name instalment option is applied to pay-as-you-go options as in both the premium is paid for in stages. The former are strips of digital options, the latter are strips of compound options. This difference is explained in the introduction to this chapter.

Example 1
An FX hedger is short EUR and long USD booked at 1.0450. A six-month instalment option (with the forward at 1.0440 and volatility at 10%) would have no initial premium but the following terms: premium trigger levels of 1.0250, 1.0200 and 1.0150 with the premium at each level 1.50% EUR (110 USD pips). If any of the trigger levels are reached, then the premium for that instalment is due. If all the levels are reached, a total of 330 USD pips will have been paid far more than the 2.72% EUR (280 USD pips) payable for the equivalent vanilla European option.

Example 2
A company wants to hedge a three-year floating-rate loan on three-month Euribor. It believes Euribor will peak at 5%. A standard interest rate cap with a strike of 5% would cost them 4% upfront. Instead they can enter a reflex cap at 5% with a trigger rate of 6%, just above the expected peak. This structure would cost the company 19 bp for every period Euribor resets below 6% and 62 bp for every period Euribor resets above 6%. Euribor would have to stay above 6% for more than 9 out of the 12 months for the standard cap to outperform the reflex cap on a present value basis. The periodic premium is therefore low when Euribor is marginally above the strike and higher when the cap is deep in-the-money the buyer is paying more for the cap when it is most valuable. The reflex cap combines a normal interest rate cap with a series of digital options that expire on every reset date. The normal cap is partially paid for by a preset amount per period (which would be 19 bp in the example) and partially by the sale of the digitals (43 bp per period). The reflex cap provides full cap protection without an immediate premium payment; costs less than a vanilla cap if never used; and is advantageous where the view is that rates will not rise dramatically above the strike, although if it does, the higher premium is only payable in those periods where the cap is deep in-the-money.

Part-contingent knock-in option

An option that only knocks-in if spot moves sufficiently against the buyer’s underlying position. The premium payable at origination is less than for a standard knock-in, but if the option is knocked-in, then an additional premium payment is required that makes the option more expensive than the standard would have been. Also known as a part contingent premium option.

Example
A hedger buys a GBP put/USD call with a strike of 1.65 and a knock-in at 1.57. The normal cost of this option is 1.70% GBP. The part-contingent structure makes the upfront premium just 0.90% but the buyer is obliged to pay an additional 2.40% GBP if the knock-in level is hit. So if sterling appreciates the option will not knock-in. If sterling depreciates but does not hit 1.57 then the buyer has no protection but has only spent 0.90%.

Reverse contingent premium option

An option whose premium is only due if the option expires at- or out-of-the-money that is, the put version of a contingent premium option. Like contingent premium options the premium can be calculated on expiry or at set points during the life of the option. In the latter case no initial premium is paid but if, subsequently, the underlying moves beyond preset trigger points set out-of-the-money relative to the strike, certain fixed premiums are payable by the holder of the option at maturity. For catastrophe insurance, the structure offers potentially zero premium protection. However, if all the trigger levels are reached, then the holder pays more in premium than the equivalent vanilla option (he pays the vanilla premium plus its financing costs). For this to have happened though, the underlying must have moved in the hedger’s favour. This makes the option useful where protection is required (put) but market view is bullish. The purchaser can elect not to make an instalment payment, in which case the option is terminated.

Thomas A. Fetherston at the University of Albama put this together at some point in time – a mix of teaching notes, core concepts, a glossary and a 109 page handy desk reference that you would end up referring to if you work with derivatives in any shape and form.

I stumbled across this resource about 5 years ago and it had been stewing invisibly in one of the many resource folders I have on my hard drive. I believe it would be a crime to sit or hide on a resource like this. The Glossary is here and I will try and post the teaching notes over the next few days after turning them into bite sized pieces as and when I get time.

I looked for Tom’s home page but a Google search on Tom’s name only pulls up his authored books, no home page that I could possibly link to.