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
= c_{0} = $2.50, Current Stock Price = S_{0} =
$25,

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

Price of Put = p_{0} = ?

We know According to Put call parity

S_{0} + p_{0} = c_{0} + X / (1 +
r)^{T}

25 + p_{0} = 2.50 + 30 / (1 + 2.5%)^{0.25}

25 + p_{0} = 2.50 + 30 / (1.025)^{0.25}

25 + p_{0} = 2.50 + 30 / 1.0061922

25 + p_{0} = 2.50 + 29.8153

p_{0} = 29.8153 + 2.50 - 25

p_{0} = 7.3153 = 7.31 (rounded to two decimal
places)

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

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