Economics

An exchange rate is quoted as price-currency per base-currency. The quote P/B means the number of units of the price (quote) currency required to buy one unit of the base currency. The base is the denominator currency whose value is being measured.

A spot rate is the price for currency delivered immediately (typically T+2 settlement). A forward rate is agreed today for the exchange of currencies at a specified future date. The forward rate is determined by the spot rate and the interest rate differential, not by expected future spot rates under no-arbitrage.

Forward points are the difference between the forward rate and the spot rate, scaled (often by 10,000 for four-decimal pairs). Forward rate = spot rate + (forward points / scaling factor). Positive points mean the base currency trades at a forward premium.

The base currency trades at a forward premium when its interest rate is lower than the price currency's rate (forward > spot). It trades at a forward discount when its interest rate is higher (forward < spot). The lower-yielding currency is always at a forward premium.

Forward(P/B) = Spot(P/B) × (1 + i_P × days/360) / (1 + i_B × days/360), where i_P is the price-currency interest rate and i_B is the base-currency interest rate. This relationship is enforced by arbitrage and requires no risk assumptions.

Value to the buyer of the base currency = (Forward_t − Forward_initial) × contract size, discounted from settlement to today at the price-currency rate. You offset the position with a new forward to the original settlement date, then present-value the gain or loss.