The idea that it is possible to purchase a foreign exchange option without paying a premium is so attractive that skepticism would be justified. A forward contract that you can effectively walk away from if it turns out badly--while still not having to pay up-front for the privilege--seems like a free lunch, which is a scarce commodity in today's efficient markets. The attractions of zero-premium options are self-evident, but what if it were possible to actually trade them in practice?
Of course, the FX options market is not really handing out free money. What is possible, however, is to structure an option so that the downside appears in other ways, and payment of premium in advance is avoided. These are not so much zero-premium as deferred premium options. All other aspects of the option, including the downside, are essentially unchanged, as we shall see.
There are many attractions to being able to avoid initial cash outlay in this manner. Many corporate treasurers are unable to pay premiums due to accounting constraints, and a company that wishes to hedge forward a number of years may well be deterred by the large price tag, even if options would have been the best choice of instrument. It would free other users from the constraint of having to sell financing options, which can lead to potentially unlimited hedge losses, just to eliminate the premium. Perhaps most importantly, many entities can use the capital tied up in the premium to achieve a much better rate of return than the 'risk-free rate' used to price the option. By paying premium in advance, they are effectively lending to the option market at this rate, and therefore losing money.
Let us take an example of a one-year, at-the-money-forward (ATMF) euro call / U.S. dollar put. Such an option might be used to hedge a short euro position, but for simplicity we will consider the option in isolation. We use current market values (at the time of writing)--spot reference USD0.97, forward outright USD0.9468, 12 month deposit rate of 6.81% and a volatility of 12%. Using these inputs, the value of the euro call option is 424 dollar pips.
The key to creating this deferred premium structure is to use synthetics--the art of combining options and/or forwards to create a payoff profile identical to a different option/forward. In our example, we wish to create a payoff profile identical to that of a purchased ATMF euro call. This can be done by buying a forward contract and combining it with a purchased ATMF put option. Below the option strike, the downside of the forward is offset by the put, and above the strike the forward provides the upside while the put is out of the money. The two positions (euro call and combined long forward/euro put) are referred to as being synthetically equivalent. If they are not identical, an arbitrage opportunity exists.
This does not solve the central problem, as the put option must still be paid for, and the premium is the same as that of the call option, i.e. 424 dollar pips. This is taken care of by synthetically creating the forward in the above trade by buying a euro call and selling a euro put with the same strike. This synthetic forward is zero cost only if struck at the forward--with options you have the flexibility to strike away from the forward, creating an up-front cash credit or deficit. In our example, if the options used to create the forward are struck at USD0.9921, the participant is locked into a rate 453 dollar pips worse than the forward. However, as this disadvantage will only be felt one year into the future, they will only receive the present value of this amount today, which is 424 dollar pips using a risk free one-year rate of 6.81%.
Thus our synthetically-created forward, struck at the carefully chosen rate of USD0.9921, has generated an up-front cash credit of 424 dollar pips, which is exactly equal to the put option premium. The entire structure is therefore zero premium, but as shown above it is synthetically equivalent to the purchased ATMF euro call option.
How do the two positions compare in practice? At first sight they seem to be different. The worst case for a euro call is if the market is at USD0.9468 or below at expiry. For the deferred premium structure, the synthetic forward struck at USD0.9921 is 453 dollar pips underwater, and the put option is at the money. It might seem that the downside is slightly larger, but this is not the case. The difference is due to the fact that the regular option's premium of 424 dollar pips is paid at the start of the period, whereas the deferred premium structure's downside is only experienced at expiry. If those 424 dollar pips were to be invested at the risk-free rate of 6.81% for the year it would earn 29 dollar pips of interest, effectively eliminating the difference.
Without the need to focus on initial cash outlay, the market participant is able to focus on the important issues such as, what is the maximum risk and break-even? What is my probability of breaking even given current market volatility? Am I comfortable with the trade-off of having a position that makes money at an accelerating rate and loses it at a decelerating rate (positive gamma) versus the effect of time decay (theta)? Freed from the need to justify its up-front outlay, the end user is able to concentrate on the issues that are important in choosing an appropriate option strategy.
This week's Learning Curve was written byChris Attfield, an analyst in the the strategic risk management advisory group atBank Onein London.