Question

Assume that Brian Co. will need to purchase 100,000 Singapore dollars (S$) in 180 days. Today’s spot rate of the S$ is $.50, and the 180‑day forward rate is $.53. A call option on S$ exists, with an exercise price of $.52, a premium of $.02, and a 180‑day expiration date. A put option on S$ exists, with an exercise price of $.51, a premium of $.02, and a 180‑day expiration date. Brian has developed the following probability distribution for the spot rate in 180 days:

                     Possible Spot Rate

                            in 180 Days                              Probability

                                 $.48                                         10%

                                 $.53                                         60%

                                 $.55                                         30%

      The probability that the forward hedge will result in a higher payment than the options hedge is _______ (include the amount paid for the premium when estimating the U.S. dollars required for the options hedge).

	0%
	10%
	30%
	70%

Answer 1

The forward hedge can be done by purchasing the 180 day forward at $0.53

For the options hedge , Brian Co. will use Call Options as they need to purchase Singapore Dollar after 180 days. The Call option with Strike price of $0.52 can be purchased at a price of $0.02

After 180 days,

If spot rate = $0.48 (probabiity = 10%)

Forward hedge will result in a net payment of $0.53 per Singapore dollar whereas

option hedge will result in Option becoming worthless and a total payment of $0.48 + $0.02 =$0.50 per Singapore dollar

So, forward hedge will result in a higher payment than the options hedge

If spot rate = $0.53 (probabiity = 60%)

Forward hedge will result in a net payment of $0.53 per Singapore dollar whereas

option hedge will result in Option getting exercised and a total payment of $0.52 + $0.02 =$0.54 per Singapore dollar

So, forward hedge will result in a lesser payment than the options hedge

If spot rate = $0.55 (probabiity = 30%)

Forward hedge will result in a net payment of $0.53 per Singapore dollar whereas

Option hedge will result in Option getting exercised and a total payment of $0.52 + $0.02 =$0.54 per Singapore dollar

So, forward hedge will result in a lesser payment than the options hedge

So, forward hedge will result in higher payment is only in 1st case with probability of 10% (2nd option)