Question

Choco Inc. buys chocolate from Switzerland and resells it in the U.S. It just purchased chocolate invoiced
at SF50,000. Payment for the invoice is due in 30 days. Assume that the current exchange rate of the
Swiss franc is $1.00. Also assume that three call options for the franc are available. The first option has a
strike price of $1.00 and a premium of $.03; the second option has a strike price of $1.03 and a premium
of $.01; the third option has a strike price of $1.06 and a premium of $.005. Choco Inc. expects a modest
appreciation in the Swiss franc.
a) (5 points) Describe how Choco Inc. could construct a bullspread using the first two options. What is
the cost of this hedge? When is this hedge most effective? When is it least effective?
b) (5 points) Describe how Choco Inc. could construct a bullspread using the first and the third options.
What is the cost of this hedge? When is this hedge most effective? When is it least effective?
c) (5 points) Given your answers to parts (a) and (b), what is the tradeoff involved in constructing a
bullspread using call options with a higher exercise price?

Answer 1

a) Bull spread is constructed by buying a call option with lower strike price and selling a call option with higher strike price.

First option has lower strike price out of the first two options. So, we will buy call option with strike price of $1.00 and sell call option with strike price of $1.03. The premium paid on purchasing the call option will be compensated by premium received on selling the call option.

Cost of the hedge = premium paid - premium received = $0.03 - $0.01 = $0.02

This hedge is most effective when spot exchange rate at expiration will be between $1.00 and $1.03. If it's higher than $1.03 then call option sold will be exercised and we will have to make payment on short call which will reduce our gain on long call. if it's between $1.00 and $1.03 then we will have payoff from long call and short call will expire worthless.

This hedge is least effective when spot exchange rate at expiration is lower than $1.00. in that situation, long call will expire worthless and we will incur cost of hedge of $0.02.

b) Bull spread is constructed by buying a call option with lower strike price and selling a call option with higher strike price.

First option has lower strike price out of the first two options. So, we will buy call option with strike price of $1.00 and sell call option with strike price of $1.06. The premium paid on purchasing the call option will be compensated by premium received on selling the call option.

Cost of the hedge = premium paid - premium received = $0.03 - $0.005 = $0.025

This hedge is most effective when spot exchange rate at expiration will be between $1.00 and $1.06. If it's higher than $1.06 then call option sold will be exercised and we will have to make payment on short call which will reduce our gain on long call. if it's between $1.00 and $1.06 then we will have payoff from long call and short call will expire worthless.

This hedge is least effective when spot exchange rate at expiration is lower than $1.00. in that situation, long call will expire worthless and we will incur cost of hedge of $0.025.

c)  trade off involved in constructing a bull spread using call options with a higher exercise price is the lower cost of hedge. instead of using option 1 & 2 or option 1 & 3 if we use option 2 & 3 with higher exercise prices to construct bull spread then cost of the hedge will be lower.

Cost of hedge with option 2 & 3 = premium paid - premium received = $0.01 - $0.005 = $0.005

Also in the question it's mentioned that Choco Inc. expects a modest appreciation in Swiss franc. So it's best to use options 2 & 3 to construct bull spread with higher exercise prices and trade off of lower cost of hedge.