Question

The call premium and put premium for K = $1000 and T = 1 year are $90 and $70 respectively. The risk-free rate is 5% per year. If there is a forward contract written on the same underlying asset and the same expiration as those of the options , what is the forward price supposed to be?

A.) $1021

B.) $1020

C.) $1019

D.) $1018

Answer 1

Using Put call Parity

Call premium + Strike price / (1 + risk free rate) = Spot price + Put premium

Spot price = Forward price / (1 + risk free rate)

Call premium + Strike price / (1 + risk free rate) = Forward price / (1 + risk free rate) + Put premium

$90 + $1000 / (1 + 5%) = Forward price / (1 + 5%) + $70

$90 + $952.38 = Forward price / (1 + 5%) + $70

Forward price / (1 + 5%) = $90 + $952.38 - $70

Forward price / (1 + 5%) = $972.38

Forward price = $972.38 * (1 + 5%)

Forward price = $1021