I am having a bit of trouble with a problem I've been given.

Consider a market which only trades a stock and forward contracts. There's only time 0 and 1.

Initial stock price S_0 is 10, the forward price F = 12, and at time 1, stock takes the price of either 11 or 14.

So I am asked to replicate a call option on the stock with strike price 13 with maturity at 1 and find the arbitrage free price of the call.

Some searching for similar problems told me to buy stock and sell short on a bond to replicate the call, but since a forward contract that can either benefit or incur a loss is in place of the bond, I am not so sure what to do. So I am replacing shorting a bond to shorting a forward contract? The problem doesn't give any probabilities on whether a stock would 11 or 14, so I am getting more and more confused.

I am still learning basics of finance, so any insights to understand the problem would be real helpful.

  • 3
    $\begingroup$ Hi there. Write down the payoffs (stock, forward) in a 2x2 matrix. Write down the payoff of the call as well. Then, ask: "How do I have to combine the payoffs of the stock and forward, so that this portfolio will yield the payoff to the call in each state of the world?" These weights tell you how much of stock, and forward, to buy. Ultimately, do you know that the present value of the forward contract should be? $\endgroup$ Jul 20 at 12:54

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