Question

A call option has a premium of $0.60, a strike price of $40, and 3 months to expiration. The current stock price is $39.60. The stock will pay a $0.80 dividend two months from now. The risk-free rate is 3 percent. What is the premium on a 3-month put with a strike price of $40? Assume the options are European style.

Answer 1

Put-Call Parity for a Dividend-Paying Stock:

Stock Price - PV(Dividend) = Call Premium - Put Premium + PV (Common Strike Price)

Common Strike Price = $ 40, Risk-Free Rate = 3 %, Tenure = 3 months, Dividend worth $0.8 is paid 2-months later, Call Premium = $ 0.6 and Put Premium = $ p and Stock Price = $ 39.6

Therefore, 39.6 - [0.8 / e^{0.03 x (2/12)}] = 0.6 - p + 40 / e^{0.03 x (3/12)}

p $ 1.497 ~ $ 1.5