A charitable organization has issued a bond that gives the holder the option to

Question

A charitable organization has issued a bond that gives the holder the option to cash in the principal as either £10,000 or €20,000. This asset can be viewed as a £10,000 bond plus a call on €20,000 with a strike price K=0.5£/€

a) Can the bond also be viewed as a € bond plus an option?

b) Explain how the two equivalent views are just an application of the Put-Call parity

c) Suppose that you observe the following:

The price of a call option on the European Euro (€) is 0.055 $/€. The price of a put option on the € is 0.045 $/€. Both options have 135 days left to expiration and a strike price of 0.85 $/€. The current spot rate is 0.89 $/€. The $-risk free rate is 3.5% and the €-risk free rate is 3.75%.

i) Is there an arbitrage opportunity? Why?

ii) Calculate the arbitrage profits and show the arbitrage transactions and

corresponding cash flows at t=0 (now) and at t=T=135 days later.

Explanation / Answer

(a) The equivalent view of a € bond plus an option is possible as given below :

In the orginal case the £ denominated bond was the underlying asset and the investor sells a call option to convert the underlying asset ( £ denominated bond ) into cash € (euros). In the equivalent the € bond which might be viewed as cash can be coupled with buying a put option that enables the investor to buy back the underlying asset ( £ denominated bond) at a fixed price in return for € cash.

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