Question

For a European put option on an index, the index level is 1,000, the strike price is 1050, the time to maturity is six months, the risk-free rate is 4% per annum, and the dividend yield on the index is 2% per annum. How low can the option price be without there being an arbitrage opportunity?

Answer 1

The Maximum Call Value Can Be C > Max [S-K, 0]

Where S = Stock Price = 1000

K = Strike Price = 1050

C = Max [ (1000 - 1050) , 0 ]  

C = Max [ -50, 0 ] = 0

When Call Value is 0 there is zero arbitrage opportunity

Now we will use the put-call parity theorem to find put premium p. As per Put-call parity theorem

c = call price = 0

S = Stock Price = 1000

K = Strike Price = 1050

r = Risk free rate = 4% = 0.04

T = Time to maturity = 06 Months = 0.5 Years

q = Dividend Pay out rate = 2% = 0.02

So, 1029.2086 = p + 990.049

p = 39.1587

So the lowest put option price can be = 39.1587 (Ans)