A forward contract

Referring to our game in section , it is easy to see that the payout of the derivative (i.e. the offer) has f(1)=s_down-k, f(2)=s_up-k and the price, p, of the offer itself is zero.¹⁴ The main question is to find the value of k.
If you substitute the value of f(1) and f(2) and p=0 in equation , you will notice that $k=s_{0}\exp(rT)$!