Global Pilot paper – for exams up to December 2012

Although I will tell you how the number of contracts has been arrived at, the Grabbe variant was removed from the syllabus and cannot now be examined.
The only option pricing that can be examined relates to share options.

However, the point is that as the exchange rate changes, so too will the price of options, but the option price will change by N(d1) x the change in the exchange rate.

So…using the 3 month transaction for example ……to make the changes cancel out, the number of options we need to deal in is the amount of the transaction (75M) divided by N(d1) (0.5386).
75M / 0.5386 = 278499814 options.
However we can only deal in contracts of 100,000 options and so the number is 2785

(The logic is exactly the same as delta hedges when we have share options. As I wrote above, share options can be examined, but the pricing of currency options is no longer in the syllabus)

In the answer to (b) the cost of a call option has been calculated as 3.1581 pence. They are buying 2785 contracts of 100,000, and so the total cost is 2785 x 100,000 x 0.031581 = 8795309. (The answer is a few 100 different because the examiner has rounded in one place and not in the other!!)

The percentage of value he has taken the total cost of the options divided by the 150M that is at risk.

For question 3, he has looked up in the normal distribution tables for 1.92, and then added 0.5 to the figure. The logic being that there is a 0.473 probability of being that many standard deviations below the average, but because the distribution is symmetrical there is a 0.5 probability of being above the average. So in total, a 0.973 probability of being above the figure.