The price of a European call option on a stock with a strike price of $50 is $6.The stock price is $51,the continuously compounded risk-free rate (all maturities)is 6% and the time to maturity is one year.A dividend of $1 is expected in six months.What is the price of a one-year European put option on the stock with a strike price of $50?
A) $8.97
B) $6.97
C) $3.06
D) $1.12

Question

Quizplus · Accepted Answer

Put-call parity is c+Ke^-rT=p+S₀˗D.In this case K=50,S₀=51,r=0.06,T=1,and c=6.The present value of the dividend,D,is 1×e^−0.06×0.5 = 0.97.It follows that p=6+50e^-0.06×1−(51-0.97)= 3.06.

The Price of a European Call Option on a Stock