28 October, 2022

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FX Options Guide - Section 22 - Basket Option

Basket Rate Option Introduction

In this section we take a look at the basket option, another different type of non-vanilla option that is not a barrier option. To get the most from this section you should first have covered the foundational FX options knowledge including the terminology of FX options, looked at some common option strategies and how options are funded and how these funding techniques are used when combining options. It would also be helpful to have covered the section on average rate options.

Basket Option

The basket option is designed to protect the domestic currency value of a portfolio of foreign currency cashflows.

A basket call option gives the holder the right but not the obligation to buy a basket of currencies in exchange for selling an amount of domestic currency. A basket put option gives the holder the right but not the obligation to sell a basket of currencies in exchange for buying an amount of domestic currency.

The basket option is used as an alternative to buying a strip of similar options, where the base currency of the basket option is the common currency of the strip of options.

For example, buying a basket call option versus a base currency of USD’s, where the basket currencies are JPY, EUR, AUD, and GBP would be an alternative to buying a strip of options consisting of a USD put / JPY call, USD put / EUR call, USD put / AUD call and a USD put / GBP call. As with the strip of options, the currency face amounts can be tailored to precisely match the exposures being hedged.

One of the attractions of the basket option is that it trades at a discount to the equivalent strip of European options. This is discussed later in “Basket Price vs European Strip Price”.

Strike Selection

One of the ways in which a basket option differs from the equivalent strip of options is in the way that the strike price is defined. Since there are several different currencies involved the strike cannot be defined in terms of a rate as with a standard European option. However, the strike price of a standard option describes the ratio of the two face amounts of the option. For example, a EUR/USD option with a strike of 1.1500, if the EUR face amount is EUR 10 mio then the USD face amount is USD 11.5 mio.

With a basket option we know the amounts of foreign currency exposures we wish to hedge. In the basket example above, we know the amounts of the exposures in JPY, EUR, AUD, and GBP. Each of these currencies can be converted back into USD’s by choosing a rate for that currency pair. The strike price of the basket option is defined in terms of an amount of base currency. So, in this case, the USD amounts converted from JPY, EUR, AUD, and GBP are summed, and this amount of USD’s is then the strike of the option.

Remember, the basket option is designed to protect the domestic currency value of a portfolio of foreign currency exposures. The strike price is defined in terms of domestic currency, and represents the worst case domestic currency amount that will be exchanged for the basket of currencies at expiration.

For a basket call option, the strike defines the amount of the base currency that the holder of the basket option would sell in exchange for buying the basket of currencies at expiration. In the case of the basket call option described above, this amount would represent the maximum amount of USD’s that the holder would be required to pay in order to buy the fixed amounts of JPY, EUR, AUD and GBP.

The At-The-Money-Forward strike would be determined by converting the fixed amounts of JPY, EUR, AUD and GBP through the outright forward rates into USD’s. The sum of the USD amounts from these for conversions would represent the strike price.

For a basket call option, if the strike amount is greater than the ATM forward strike then the option will be more Out-Of-The-Money, since it would be less favourable for the holder of the option to give up a greater amount of USD’s in order to buy the basket currencies.

Similarly, for a basket put option, if the strike amount is less than the ATM forward strike then the option will be more Out-Of-The-Money, since it would be less favourable for the holder of the option to receive a lesser amount of USD’s in order to sell the basket currencies.

One of the ways in which the basket option differs from the equivalent strip of standard options is in the relative lack of flexibility in which the strike prices can be defined. With a strip of standard options the strike prices of the individual options can be chosen such that the different options are either more out or more in the money relative to each other. With the basket option the strike defines the percentage in or out of the money basket option is. Strikes for individual currencies within the basket are meaningless, and by definition, each of the component currencies are ITM or OTM by the same degree.

Exercise

At expiration, the decision whether or not to exercise the basket option will depend upon the base currency value of the basket of currencies when converted through spot. In the case of the basket call option, each of the basket currencies are translated through spot into the base currency. There are two possible outcomes:

If the sum of the base currency amounts is greater than or equal to the strike amount then the holder will exercise the call option. This is because the holder of the basket call option benefits by giving up a smaller amount of USD’s to buy the basket of currencies than is possible in the spot market.
If the sum of the base currency amounts is less than the strike amount then the holder will allow the option to expire, and will instead buy the JPY, EUR, AUD and GBP in the spot market, as this will result in giving up a smaller amount of domestic currency.

For a basket put option, the base currency amount would represent the minimum amount of base currency that the holder would receive in exchange for selling the basket of currencies. At expiration, each of the basket currencies are translated through spot into the base currency. If the sum of these base currency amounts is less than or equal to the strike amount then the holder will exercise the option. If the sum of these amounts is greater than the strike amount then the holder will simply exchange the basket of currencies for this amount of base currency in the spot market, as this will result in receiving a larger amount of base currency in exchange for the basket of currencies.

If it is preferred, the holder of the option can agree to have the option cash settled at expiration. This may be appropriate if the option is being used to hedge translation exposures.

Basket Price vs. European Strip Price

For the risk manager who needs to protect the domestic currency value of a portfolio of foreign currency exposures, the basket option is a cost effective alternative to a strip of European options.

The discount of the basket option relative to the strip of standard options represents the fact that the basket precisely hedges the exposure, whereas the strip of options over-hedges the exposures when considered as a whole. For the purposes of this example, assume that in the above basket call option, the JPY, EUR, AUD and GBP exposures represent equal USD amounts. If at expiration, the USD/JPY and EUR/USD components finished 10% ITM with respect to the strike, and the AUD/USD and GBP/USD finished 10% OTM with respect to the strike, then the basket option would finish ATM, as the currency moves cancel each other out. However, with the equivalent strip of standard options the USD/JPY and EUR/USD options would finish ITM and be exercised, whilst the AUD/USD and the GBP/USD would finish OTM and expire worthless. Therefore, the strip of standard options would have resulted in a greater return than for the basket option.

In this example the basket option has finished ATM, but it has precisely protected the domestic value of the portfolio of foreign currency exposures. The greater return that the strip of standard options provides represents the amount by which the strip outperforms the exposures. The extra cost of the strip represents the amount being spent on trying to outperform the exposures, which can be thought of as a limited form of speculation.

Basket Option Summary

The basket option provides a precise hedge for multi-currency exposures, and is cost effective alternative to the equivalent strip of standard options.