Question

please show the step by step and what formula used, thanks.

ww. 16) You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10 %. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co. 16) What would have been the cost of a protective put portfolio?

Answer 1

Protective Put position = P + S = Long (buy) put option + long (buy) stock

S0 = $ 50; K = $ 50; u = 1 + 10% = 1.1; d = 1 - 10% = 0.9; Su = u x S = 1.1 x 50 = $ 55; Sd = d x S0 = 0.9 x 50 = $ 45; r = 5%

Risk neutral probability of up state = p = (1 + r - d) / (u - d) = (1 + 5% - 0.9) / (1.1 - 0.9) = 0.75

Pu = max (K - Su, 0) = max (50 - 55, 0) = 0

Pd = max (K - Sd, 0) = max (50 - 45, 0) = 5

Hence, price of the put option today = [p x Pu + (1 - p) x Pd] / (1 + r) = [0.75 x 0 + (1 - 0.75) x 5] / (1 + 5%) = $ 1.19

Hence, cost of a protective put portfolio = P + S0 = 1.19 + 50 = $ 51.19