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Given that the payoff of a forward contract with strike K and maturity T has the payoff ST - K, how do I prove that the initial price of this contract is S0 - K*B0, where B0 is the price of a bond that pays $1 at time T?

I know that the strike price of a stock at time T is equal to S0 / B0 but I am not sure how to use this to find the initial price of the forward contract.

  • What is B0 supposed to be here ? – ApplePie Feb 16 at 21:26
  • just edited the post thanks! – ss98 Feb 16 at 21:32
  • massive hint: how does this relate to the risk free interest rate? – MD-Tech Feb 16 at 21:35
  • Initial price will depend on other factors depending on asset class / underlying asset (e.g. convenience yield, dividend yield, etc). The underlying should probably be specified, at least broadly (e.g. single-name forward, bond forward, etc). – ApplePie Feb 16 at 21:35
  • @ApplePie i get the feeling that the bond might be being used as the risk free rate – MD-Tech Feb 16 at 21:36
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The forward price on initial date corresponds to the initial price of the strategy that gives this payoff at times T. So here is the strategy:

  • You buy the asset at time 0. It costs S0.
  • You sell a bond with nominal K*B0. At maturity, you will pay K.

At initial time, the strategy value is S0-K*B0.

At maturity date, the strategy value will be your payoff ST-K.

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