What exactly is being conveyed here? I don't really understand how the above formula locks in a price.

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The fair forward ZCB price is given as \(P_{tTS}=\frac{P_{tS}}{P_{tT}} \) and there's a bullet point in the slides saying "economically, the bond forward price allows one (at \(t\)) to lock into a price for \(P_{TS}\) (at \(T\))".

What exactly is being conveyed here? I don't really understand how the above formula locks in a price.

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The ZCB forward is a contract which allows one to lock into a price at time \(t\) for the bond at time \(T\). We can see this in the formula for the fair forward price. The fair forward price is the price one will pay for \(P_{TS}\) at \(T\), however it can be calculated at time \(t\) since both \(P_{tT}\) and \(P_{tS}\) are measurable at time \(t\). One therefore 'locks in' to this future price that one will pay for the bond by agreeing at time \(t\) to pay \(P_{tTS}\) for the bond at time \(T\).

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