**Notes:**

1. This net receipt is effectively the minimum receipt as if the spot rate on 26 August is anything less than the exercise price of £ 0.79250/€1, the options can be exercised and approximately £3,461,094 will be received. Small changes to this net receipt may occur as the €25,000 underhedged will be converted at the spot rate prevailing on the 26 August transaction date. Alternatively, the underhedged amount could be hedged on the forward market. This has not been considered here as the underhedged amount is relatively small.

**2. **For simplicity it has been assumed that the options have been exercised. However, as the transaction date is prior to the maturity date of the options the company would in reality sell the options back to the market and thereby benefit from both the intrinsic and time value of the option. By exercising they only benefit from the intrinsic value. Hence, the fact that American options can be exercised at any time up to their maturity date gives them no real benefit over European options, which can only be exercised on the maturity date, so long as the options are tradable in active markets. The exception perhaps is traded equity options where exercising prior to maturity may give the rights to upcoming dividends.

**Summary**

Much of the above is also essential basic knowledge. You are unlikely to be given the spot rate on the transaction date. However, the future spot rate can be assumed to equal the forward rate which is likely to be given in the exam. The ability to do this may earn up to six marks in the exam. Equally, another one or two marks could be earned for reasonable advice.

### Foreign exchange options – other terminology

This article will now focus on other terminology associated with foreign exchange options and options and risk management generally. All too often students neglect these as they focus their efforts on learning the basic computations required. However, knowledge of them would help students understand the computations better and is essential knowledge if entering into a discussion regarding options.

**Long and short positions**

A **‘long position’** is one held if you believe the value of the underlying asset will rise. For instance, if you own shares in a company you have a long position as you presumably believe the shares will rise in value in the future. You are said to be long in that company.

A **‘short position’** is one held if you believe the value of the underlying asset will fall. For instance, if you buy options to sell a company’s shares, you have a short position as you would gain if the value of the shares fell. You are said to be short in that company.

#### Underlying position

In our example above where a UK company was expecting a receipt in €, the company will gain if the € gains in value – hence the company is long in €. Equally the company would gain if the £ falls in value – hence, the company is short in £. This is their **‘underlying position’**.

To create an effective hedge, the company must create the opposite position. This has been achieved as, within the hedge, put options were purchased. Each of these options gives the company the right to sell €125,000 at the exercise price and buying these options means that the company will gain if the € falls in value. Hence, they are short in €.

Therefore, the position taken in the hedge is opposite to the underlying position and, in this way, the risk associated with the underlying position is largely eliminated. However, the premium payable can make this strategy expensive.

It is easy to become confused with option terminology. For instance, you may have learnt that the buyer of an option is in a long position and the seller of an option is in a short position. This seems at variance with what has been stated above, where buying the put options makes the company short in €. However, an option buyer is said to be long because they believe that the value of the option itself will rise. The value of put options for € will rise if the € falls in value. Hence, by buying the €/£ put options the company is taking a short position in €, but is long the option.

#### Hedge ratio

The hedge ratio is the ratio between the change in an option’s theoretical value and the change in the price of the underlying asset. The hedge ratio equals N(d_{1}), which is known as delta. Students should be familiar with N(d_{1}) from their studies of the Black-Scholes option pricing model. What students may not be aware of is that a variant of the Black-Scholes model (the Grabbe variant – which is no longer examinable) can be used to value currency options and, hence, N(d_{1}) or the hedge ratio can also be calculated for currency options.

Hence, if we were to assume that the hedge ratio or N(d_{1}) for the €/£ exchange traded options used in the example was 0.95 this would mean that any change in the relative values of the underlying currencies would only cause a change in the option value equivalent to 95% of the change in the value of the underlying currencies. Hence, a €0.01 per £ change in the spot market would only cause a €0.0095 per £1 change in the option value.

This information can be used to provide a better estimate of the number of options the company should use to hedge their position, such that any loss in the spot market is more exactly matched by the gain on the options:

Number of options required = amount to hedge/(contract size x hedge ratio)

In our example above, the result would be:

€4.4m/(€0.125m x 0.95) ≈ 37 options

### Conclusion

This article has revisited some of the basic calculations required for foreign exchange futures and options questions using real market data, and has additionally considered some other key issues and terminology in order to further build knowledge and confidence in this area.

**William Parrott, freelance tutor and senior FM tutor, MAT Uganda**