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

From Interest rate parity. the two year forward rate should be

F = 5.9*1.02² / 1.03²

= 5.786 HKD/CAD

So, after 2 years the Intrinsic value of the put option at expiry = 6.5 - 5.786 HKD/CAD

=0.714 HKD/CAD

So, the strategy is as follows :

Today : Borrow (5.5613+0.4) HKD i.e. 5.9613 HKD @ 2% for 2 years . After 2 years, you have to repay = 5.9613*1.02² = 6.2022 HKD

Buy the put using 0.4 HKD and convert remaining 5.5613 HKD to CAD to get 5.5613/5.9 = 0.9426 CAD

Invest 0.9426 CAD in canada @ 3%

After two years

0.9426 CAD will grow to 0.9426* 1.03² =1 CAD

Now, if Exchange rate is more than strike price say 7 HKD/CAD

let the option expire, sell the 1 CAD in market and get 7*1 = 7 HKD

Repay 6.2022 HKD and you have a riskless profit (arbitrage) of 0.7978 HKD

If Exchange rate is less than strike price say 6 HKD/CAD

exercise the option sell the 1 CAD using the option and get 6.5 HKD

Repay 6.2022 HKD and you have a riskless profit (arbitrage) of 0.2978 HKD

Presented in tabular form as below :

		After 2 years
Time	Today	if exch rate > 6.5 HKD/CAD, say 7 HKD/CAD	if exch rate <6.5 HKD/CAD, say 6 HKD/CAD
Actions	Borrow 5.9613 HKD @ 2% for 2 years,	Let option expire	Exercise option
	Repayment after 2 years =6.2022 HKD	Sell 1 CAD at market to get 7 HKD	Sell 1 CAD @ 6.5 HKD to get 6.5 HKD
	Buy put option @ 0.4 HKD	Repay 6.2022 HKD loan	Repay 6.2022 HKD loan
	Convert remaining 5.5613 HKD to CAD to get 0.9426 HKD	Profit of 0.7978 HKD	Profit of 0.2978 HKD
	and invest in Canada @ 3% for 2 years, after 2 years to get 1CAD