Consider a stock index currently standing at 2,100. The dividend yield on the in

Question

Consider a stock index currently standing at 2,100. The dividend yield on the index is 3% per annum and the risk-free rate is 1%. A 3-month European call option on the index with a strike price of 2,000 is trading at $105.91. What is the value of a 3-month European put option with a strike price of 2,000? (Hint: put-call parity) Consider a stock index currently standing at 2,100. The dividend yield on the index is 3% per annum and the risk-free rate is 1%. A 3-month European call option on the index with a strike price of 2,000 is trading at $105.91. What is the value of a 3-month European put option with a strike price of 2,000? (Hint: put-call parity)

Explanation / Answer

In this case.....

S0 = 2,100, q=0.03, r=0.01, T=0.25, K=2,000 and c=  $105.91

Using put-call parity

c + Ke-rT = S0e-qT

or

p=c+ke-rT- S0e-qT

Substituting:

p= 105.91 + 2,000e-0.25*0.01 - 2,100e-0.25*0.03

p=2100.91-2084.30

p=16.60

The put price is 16.60.

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