Question

Consider a two-year European put on Canadian Dollar (CAD). The strike price of the put is 6.50
HKD(Hong Kong Dollar)/CAD. The risk-free rate is 2% per annum in Hong Kong and 3% per annum
in Canada. The current exchange rate is 5.90 HKD/CAD. The put currently sells for $0.4 in Hong
Kong. Is there an arbitrage for Hong Kong investors? If so, show an arbitrage strategy. (To show the
arbitrage, present the table listing actions and resulting cash flows)

Answer 1

Calculation of 2 year forward rate:

Forward rate = Spot rate [(1 + Rh) / (1 + Rf)]^2

where Rh = Interest rate for home country

Rf = Interest rate for foreign country

Forward rate = 5.90 [(1 + 0.02) / (1 + 0.03)]^2

= 5.90 (1.02 / 1.03)^2

= 5.79 HKD/CAD

Since strike price for put option is 6.50 HKD/CAD, arbitrage exists.

In given case since strike price is higher than forward rate as calculated, put option will be exercised. Suppose 100 put options are purchased, arbitrage gain will be calculated as below:

Action	Cash flow
Buy 100 put options @ $0.40	-40 HKD
Gain from put option
(6.50 - 5.79) * 100	71 HKD
Arbitrage gain	31 HKD