Question

The price of a non-dividend paying stock is $19 and the price of a three-month European put option on the stock with a strike price of $20 is $1.80. The risk-free rate is 4% per annum. What is the price of a three-month European call option with a strike price of $20? Is the call option in the money or out of the money? Explain Is the put option in the money or out the money? Explain

Answer 1

Using put-call parity,

cash + call = Stock + put

20 / (1+4% x 3/12) + call = 19 + 1.80

Therefore, call = $ 1.00

Price of a three-month European call option with a strike price of $20 = $ 1.00

Option is said to be in the money, if it has positive value, had it been exercised now.

Strike price of call option is $20

Current spot price is $19

Therefore, call is out of the money

Strike price of put option is $20

Current spot price is $19

Therefore, put option is in the money

Since put option is option to sell the asset at strike price. Therefore if put option is exercised now, it has positive value $1