42.5:Suppose that a stock will pay a dividend of $2 in 4 months. A call option o

Question

42.5:Suppose that a stock will pay a dividend of $2 in 4 months. A call option on the stock has a strike price of $33 and will expire in 6 months. Four months from now, the stock price is expected to be $35 and the price of the call will be $3 after the dividend is paid. The annual continuously compounded risk-free interest rate r is 0.03. If the call option is unexercised, what will be the value 4 months from now of a put option on the stock with a strike price of $33 and time to expiration of 6 months? [answer:$0.8354]

Explanation / Answer

Put call parity states that

S+P-D=C+Xe^(-rt)

where D is dividend, S is stock price, P is put option premium, C is call option premium, X is exercise price, t is time to expiry, r is risk free rate

S-D=35

t=2/12=0.1666

X=33

C=3

r=0.03

Hence, 35+P=3+33*e^(-0.03*1/6)

So, P=3+33*e^(-0.03*1/6)-35

P=0.8354

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