Question

(Currency options) Suppose you are importing clothes from Japan and you have Yen 6,250,000 payable due in 90 days. The current spot rate is $0.005 per Yen. The 90-day forward rate is 0.0054. Currently, the currency option market offers Yen call option with a maturity date in 90 days and a strike price of 0.0053. The premium of this option is $0.0002/yen. Note that one unit of Japanese Yen option contract is 6,250,000 Yen. You are considering two possible hedging methods: (a) use forward, (b) use option.

(1) You expect that the actual spot rate in 90 days would be 0.006 $/Yen. Which hedging method, (a) or (b), would you choose? Support your answer by calculating potential gain or loss of each method.

(2) If the actual spot rate in 90 days turned out to be 0.005 $/Yen, then which hedging method would have been a better choice (evaluate each choice by calculating ex post gains or losses)? Why? (Note that “wait and use spot market later” is not considered.)

(3) You expect that the actual spot rate in 90 days would be higher than 0.0052 for sure. Which method would you choose, options or forward? Explain.

Answer 1

Answer-(1)

	Forward hedge	Option Hedging
Payment Exposure in 90 days	Yen 6,250,000	Yen 6,250,000
90-day forward rate	$0.0054 / yen
Payment Under Forward hedge	$33,750
[Yen 6,250,000*90 days forwars rate]
90 days call option		$0.0053/ yen
Option Premium		$0.0002/yen
Option Premuim to be paid		$1,250
[Yen 6250000* $0.0002 per yen]
Total payment under Option hedging		$34,375
[Yen 6250000*90 days call option]+[option premium paid]
actual spot rate in 90 days	0.006 $/Yen	0.006 $/Yen
Payment would have been made if no hedging has been taken(A)	$37,500	$37,500
[Yen 6,250,000* $0.006 per yen]
Payment made under hedging (B)	$33,750	$34,375
Gain/(loss) (A-B)	$3,750	$3,125

Forward hedging would have been better.

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Answer(2)

	Forward hedge	Option Hedging
Payment Exposure in 90 days	Yen 6,250,000	Yen 6,250,000
90-day forward rate	$0.0054 / yen
Payment Under Forward hedge	$33,750
[Yen 6,250,000*90 days forwars rate]
90 days call option		$0.0053/ yen
Option Premium		$0.0002/yen
Option Premuim to be paid		$1,250
[Yen 6250000* $0.0002 per yen]
if actual spot rate in 90 days	0.005 $/Yen	0.005 $/Yen
	Note-Forward contract cannot be cancelled	Note-if actual rate is 0.005$/ yen at the end of 90 days then you will not exercise your call option and you will buy the Yen from market at cheaper rate of $0.005/yen instead of buying it @0.0053$/YEN
Hence payment under option hedge		$32,500
[Yen 6,250,000* $0.005 per yen]+option premium already paid]
Payment would have been made if no hedging has been taken(A)	$31,250	$37,500
[Yen 6,250,000* $0.005 per yen]
Payment nade under hedging (B)	$33,750	$32,500
Gain/(loss) (A-B)	-$2,500	$5,000

Opinion-Option hedging method would have been a better choice

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Answer(3)

Under Forward contract the Effective cost of one yen = $0.0054.

Under Option Hedging the MINIMUM cost of one yen = Option strike price + Premium paid = $0.0053+ $$0.0002=$0.0055

You expect that the actual spot rate in 90 days would be higher than 0.0052 for sure.

In such case the Forward contract will be better option.

Because if we choose the option hedging and the spot rate after 90 days is Say $0.0053 (i.e. more than $0.0052/yen) still then the Minimum cost is $0.0055/yen under option hedge.

hence FORWARD HEDGE WILL BE BETTER as per yen cost is less under forward cotract.