Question

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

                        Possible Spot Rate

                     in 180 Days for SGD                     Probability

                                 $.48                                         10%

                                 $.53                                         60%

                                 $.55                                         30%

      The probability that a 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).

Answer 1

To Purchase SGD 100,000 in 180 days

spot rate - $0.50

180 day forward - $0.53

Call option exercise price - $0.52 premium $.02

Put option $0.51 premium $0.02

Relevant option in the given case is call option as it is the option to purchase an underlying value at the given purchase price

Therefore relevant exercise price and premium is $0.52 premium $0.2

180 day forward rate - $0.53 ~ $0.53 * SGD 100,000 = $ 53,000

Call option at expiration $0.52 premium $0.02 ~ $0.54 ($0.52 + $0.02) * SGD 100,000 = $ 54,000

Considering the above probability that the forward hedge will result in higher payment than option hedge is zero as under call option $1,000 is paid more at the expiry of 180 days