Question

An options exchange has a number of European call and put options listed for trading on GEMCO stock. You have been paying close attention to two put options on GEMCO, one with an exercise price of $40 and the other with an exercise price of $42. The former is currently trading at $2.20 and the latter at $4.50. Both options have a remaining life of six months. The current price of GEMCO stock is $41 and the risk-free rate is 4% p.a., continuously compounded.

Explain the arbitrage strategy you would employ to exploit this situation to earn risk-free profits. You should assume that you can borrow or lend at the risk-free rate, short sell shares if necessary and do not face any transaction costs.

Thank you :)

Answer 1

Buy put with strike 40 and sell put with strike 42
Net premium received=4.5-2.2=2.3
Inbvest at risk free rate for 3 months
the amount becomes 2.3*e^(4%*6/12)=2.346463082

Lets say the price at expiry is S
payoff=-max(42-S,0)+max(40-S,0)

When S<40 payoff=-2
When S>40 and S<42 payoff=S-42
When S>42 payoff=0

Total profit when S<40: -2+2.346463=0.346463
Total profit when 42>S>40: S-42+2.346463=S-39.653537 This will be more than zero
Total profit when S>42: 0+2.346463=2.346463

We see this stragey will always be profitable