Determine value of put option with same strike & expiration

Question

Stock price is $98; and European call option struck at $100 along with an expiration of nine months has a value of $9.07. There nine-month, compounded continuously, interest rate is 4.5%. So find out the value of the put option with the same strike and expiration?

Answer 1

The expression of find out Put–call parity is:

Call price–Put price = Stock price– Strike price x (present valued from expiration)).

By rearranging the given expression we get

Put price = 9.07 − 98 + 100 e−0.045×0.75

= 7.75.

Hence the put must be worth $7.75.