Question

A European call option and put option on a stock both have a strike price of $20 and an expiration date in three months. Both sell for $2. The risk-free interest rate is 5% per annum, the current stock price is $25, and a $1 dividend is expected in one month. Identify the arbitrage opportunity open to a trader.

Answer 1

1. Calculation of Future Spot Price

FSP = ( Spot Price - Dividend) X Present Value Factor ( 5 % p.a , 3m ) i.e,

= ( Spot Price - Dividend) X Present Value Factor ( 1.25 % , 3 ) ( 5 % for 12m , 1.25 % for 3m)

= $ (25-1) X 0.96

= $ 23.12

Strike Price = $ 20

Call Option

Strike Price = $ 20

FSP = $ 23.12

Option = Excersises  

Gross Payoff = Strike Price - FSP

= $ 23.12 -20

= $ 3.12

Net Payoff = Gross Payoff - Option Price

= $ 3.12 - 2

= $ 1.12

PUT OPTION

Strike Price = $ 20

FSP = $ 23.12

Option = Lapses

Gross Payoff = Option Price

= 2

So Trader has to Hold the Call Option Which gives him Profit of $ 1.12 , and Write the Put option for income of option value $ 2