What has gone wrong?

Think about this: Suppose I am selling you this offer for k dollars. Then I have to give you the stock at time T, what I could have done (among many methods) is that:

1.

borrow s₀ dollars at time zero and buy 1 share of stock.

2.

put the stock into my safe until time T.

3.

at time T, I give you the stock, you give me money (k dollars).

4.

but I have to pay back my loan at time T, which is $s_{0}\exp(rT)$, so if I set $k>s_{0}\exp(rT)$ then I am sure I will earn money without any risk. (the keyword here is `without any risk')

How about you, the buyer of this offer? Let's take a look on what you could have done if $k<s_{0}\exp(rT)$.

1.

at time zero you would accept the offer at price k dollars (to be paid at time T).

2.

  also at time zero, sell the stock you are going to have at time T⁴ at any price $\kappa$ such that $k e^{-rT}<\kappa <s_{0}$. (Anyone will buy this since this price is LESS than the stock price!)

3.

put the money mentioned in in a bank and at time T you will have $\kappa e^{rT}$.

4.

but you will (at time T) have to pay k dollars to the seller of the offer (i.e. me); nevertheless, you still makes a net profit of $\kappa e^{rT}-k>0$ without any risk.

Conclusion: The CORRECT answer for k in game is

$$\large {k=s_{0} e^{rT}}$$ (1)

The above formula is right since we have to make sure that no one makes any profit risk free.⁵ With this discovery, correct pricing of derivatives⁶ just reduces to the modelling of stock market and trying to find a portfolio that exactly simulates the payout of the derivative.