Question

A 3 month calls cost 2.50 with a strike of 30 on a stock which costs $25. If the risk free rate is 2.5% what should be the cost of a 3 month put with a strike of 30?

Answer 1

Risk free rate = r = 2.5%, Strike price = X = $30, Price of Call = c₀ = $2.50, Current Stock Price = S₀ = $25,

Time period = T = 3 months = 3/12 year = 0.25 year

Price of Put = p₀ = ?

We know According to Put call parity

S₀ + p₀ = c₀ + X / (1 + r)^T

25 + p₀ = 2.50 + 30 / (1 + 2.5%)^0.25

25 + p₀ = 2.50 + 30 / (1.025)^0.25

25 + p₀ = 2.50 + 30 / 1.0061922

25 + p₀ = 2.50 + 29.8153

p₀ = 29.8153 + 2.50 - 25

p₀ = 7.3153 = 7.31 (rounded to two decimal places)

Cost of three month put with strike of 30 = $7.31