17. Consider a stock index currently standing at 250·The dividend yield, g\" on

Question

17. Consider a stock index currently standing at 250·The dividend yield, g" on the index is 4% per annum and the risk-free rate, r , is 6% per annum. A 3-month European Call option on the index with a strike price of 245 is currently worth $10. We want to value a 3-month European put option on the index with a strike price of 245 a) The put-call parity relationship for European-style options on a non-dividend paying stock with price So and strike K sc-Ke-t-p + So, where r is the risk-free rate and c & p are the value of the call and the put, respectively. What is the put-call parity relationship for the dividend yielding index? Carefully define your notation. b) What is the value of the put in this question?

Explanation / Answer

a)

C + X*e-r*t = P + S0*e-q*t

q = implied dividend yield

b)

P = C + X*e-r*t - S0*e-q*t

t = 3/12 = 0.25

P = 10 + 245*EXP(-6%*0.25) - 250*EXP(-4%*0.25)

= 3.84

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