Homework SourseA European call option and put option on a stock both have a
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.
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.
Solution
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
