Question

Instructions: Show all calculations in detail. No partial credit will be given for just answers.

3. An importer of Swiss watches has an account payable of CHF750,000 due in 90 days. The following data is available:

Rates and prices in US-cents/CHF.

              Spot rate: 71.42 cents/CHF

90-day forward rate: 71.14 cents/CHF

US –dollar 90-day interest rate: 3.75% per year

Swiss franc 90-day interest rate: 5.33% per year

Option Data in cents/CHF

_______________________________                        

Strike                     Call                  Put

70                          2.55                1.42

72                          1.55                2.40

_______________________________

1. Assess the USD cost to the importer in 90 days if it uses a call option to hedge its CHF750,000 account payable. Use the call with a strike price of 72 cents/CHF and include the option call premium in the cost.

2. What will be the cost of the payable in 90 days if a forward contract is used?

c. By how much must the CHF weaken relative to the USD, from 71.42 cents/CHF before the call option provides a lower cost than the forward hedge?

Answer 1

Solution:

a.

Position taken by the trader is of call buyer, having the exercise price of 72 US-cents and the option premium of 1.55 US-cents.

The current market price (CMP) as on expiry (after 90 days) is not given. Therefore there can be the two situations – on expiry the CMP is more than the exercise price or on expiry the CMP is less than the exercise price.

Case 1: The CMP on expiry is 75 US-cents (CMP > Exercise price).

The call buyer will exercise the option and the rate at which the trader hedge his payables is Exercise price + option premium (72 US-cents + 1.55 US-cents = 73.55 US-cents).

The total amount of US-cents required paying to the bank by the importer on expiry in order to require the CHF can be calculated as follows:

CHF 750,000 * 73.55 = 55,162,500 US-cents

Hence, the total US-cents payable to the bank is 55,162,500 US-cents.

Case 2: The CMP on expiry is 70 US-cents (CMP < Exercise price)

The call buyer will not exercise the option and the rate at which the trader hedge his payables is CMP on expiry + option premium (70 US-cents + 1.55 US-cents = 71.55 US-cents).

The total amount of US-cents required paying to the bank by the importer on expiry in order to require the CHF can be calculated as follows:

CHF 750,000 * 71.55 = 53,662,500 US-cents

Hence, the total US-cents payable to the bank is 55,662,500 US-cents.

Note: As the CMP on expiry are the values based on the assumptions, therefore if the CMP on expiry changes that results in the change of total US-cents payable.

b.

If the importer undertakes the forward contract from the bank, he requires to pay to the bank US-cents in order to receive the CHF can be calculated as follows:

CHF 750,000 * 71.14 = 53,355,000 US-cents

Hence, the total US-cents payable to the bank is 53,355,000 US-cents.

90 days bank forward rate is 1 CHF = 71.14 US-cents

c.

In order to have lower cost on the option contract than the forward contract, the CMP on the expiry for the call option having the exercise price of 72 US-cents is to be less than 69.59 US-cents, so that the total of CMP on expiry and the option premium comes to be less than the forward rate quoted by the bank so that the overall US-cents payable to the bank is less in the option contract.