Derivatives

F0(T) = S0(1 + r)^T — the spot compounded forward at the risk-free rate; any other price permits carry arbitrage.

F0(T) = (S0 − γ0 + θ0)(1 + r)^T: subtract the PV of benefits (income, convenience yield) and add the PV of costs (storage) before compounding.

At initiation the forward price is the agreed rate (set so value = 0). The value is the contract's worth to a party, which is zero at the start and changes as the spot/forward moves thereafter.

Vt(long) = (Ft − F0)/(1 + r)^(T−t): the discounted difference between the new forward price for delivery at T and the locked-in original price.

F0(T) = (S0 − PV(dividends))(1 + r)^T: subtract the present value of dividends expected during the contract before compounding spot forward.