Question

# A European call option and put option on a stock both have a strike price of...

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.

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

#### Earn Coins

Coins can be redeemed for fabulous gifts.