Question

1. Mazzi Corp. shares are currently trading at RM14.00 each. A three-month put option on this share is priced RM0.50 at a strike price of RM15.00. The risk free interest is 10% per annum for all maturities. Observing this data, identify and calculate what are the arbitrage opportunities available.

Answer 1

No arbitrage put option premium =

E = Exercise price or strike price = RM 15.00

S0 = Current share price = RM 14.00

r = 10% per annum

t=3 month or 3/12 year

hence , No arbitrage put option premium =

But the actual traded put option premium = RM 0.50

Since the put option is under priced , hence arbitrage gain can be obtained by Buying a put option.

Follow the following steps to get Arbitrage gain-

Step-1 :Buy a put option by paying RM 0.50 and also buy a share at its current price RM 14.

Total Initial Amount needed = RM 0.50+RM 14 = RM 14.50.

Borrow RM 14.50@10% interest paer annum for 3 months.

Step-2: After 3 months amount to be paid for borrowing of RM 14.50, alond with interest = RM 14.50+[RM 14.50*10%*3/12] = RM 14.8625.

Step-3: If after 3 month the market price per share is more than RM 15, then the arbitrageur will sell the share in the market and in case it is below the RM 15 , then the arbitrageur will exercise his Put option and will sell the share @RM 15 as the put option bought.

Hence Minimum price to be get by selling the share as per Put option is RM 15.

Step-4: Minimum Arbitrage gain after 3 month = Receive RM 15-Pay RM 14.8625 = RM 0.1375