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
C
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 .
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