The difference is measured in rupees and paid in dollars, which is why the formula divides by the fixing and not by the contract rate.
An NDF settles in dollars, for the difference between the contract rate and the fixing rate, applied to the dollar notional and divided by the fixing rate: settlement = notional × (contract rate − fixing) ÷ fixing. On an illustrative USD 10,000,000 six-month USD/INR NDF struck at 84.11, a fixing of 82.50 means the bank pays the company USD 195,152. Combined with buying the rupees at the fixing, that locks the company's cost at exactly USD 10,000,000, an effective rate of 84.11, wherever the rupee ends up.
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A non-deliverable forward exists because some currencies cannot be freely delivered offshore. The Indian rupee, the Brazilian real, the Korean won and the Taiwan dollar are the usual examples. Instead of exchanging the two currencies at maturity, the parties compare the agreed rate with an official fixing two business days earlier and one pays the other the difference in a deliverable currency, almost always dollars. Treasurers meet NDFs when hedging the costs of a subsidiary in one of these markets, and the settlement formula is where most of the confusion lies, because the difference is measured in rupees and paid in dollars.
| Input | Value |
|---|---|
| Notional | USD 10,000,000 |
| Spot USD/INR at trade date | 83.40 |
| Rupee interest rate, actual/365 | 6.20% |
| Dollar interest rate, actual/360 | 4.40% |
| Days to settlement | 182 |
| Company's position | Sells USD, buys INR (protects against a stronger rupee) |
| Fixing two business days before settlement | 82.50 |
Forward = spot × (1 + rINR × days ÷ 365) ÷ (1 + rUSD × days ÷ 360)
= 83.40 × (1 + 6.20% × 182 ÷ 365) ÷ (1 + 4.40% × 182 ÷ 360) = 84.1074, dealt at 84.11
The forward sits 0.71 rupees above spot because rupee rates are higher than dollar rates; the working is the same as for any FX forward rate. In practice the offshore NDF market sets its own implied rupee yield, which can differ from the onshore rate, so the bank's quote is the number that counts. The hedge covers 10,000,000 × 84.11 = INR 841.1m of costs.
Settlement (USD) = notional × (contract rate − fixing) ÷ fixing
= 10,000,000 × (84.11 − 82.50) ÷ 82.50 = 10,000,000 × 1.61 ÷ 82.50 = USD 195,152, paid by the bank to the company
Excel: =Notional*(Contract-Fixing)/Fixing
Why divide by the fixing? The rupee difference is real: at 84.11 the company would have received INR 841.1m for its dollars, at 82.50 it would receive only 825.0m, a shortfall of INR 16.1m. That shortfall has to be converted into dollars at the only rate both sides agree on at maturity, the fixing. INR 16.1m ÷ 82.50 = USD 195,152.
Dollars needed to buy INR 841.1m in the onshore market at the fixing = 841,100,000 ÷ 82.50 = USD 10,195,152
Less the NDF receipt = 10,195,152 − 195,152 = USD 10,000,000
Effective rate = 841,100,000 ÷ 10,000,000 = 84.11
The two legs cancel because the settlement is computed at the same rate at which the rupees are bought. That is the whole design of the instrument: a cash-settled forward that behaves like a deliverable one, provided the company can actually trade near the fixing.
| Fixing | Cost of INR at fixing, USD | NDF settlement, USD | Net cost, USD | Effective rate |
|---|---|---|---|---|
| 80.00 | 10,513,750 | 513,750 | 10,000,000 | 84.11 |
| 82.50 | 10,195,152 | 195,152 | 10,000,000 | 84.11 |
| 84.11 | 10,000,000 | 0 | 10,000,000 | 84.11 |
| 86.00 | 9,780,233 | −219,767 | 10,000,000 | 84.11 |
| 88.00 | 9,557,955 | −442,045 | 10,000,000 | 84.11 |
The payoff is not symmetric in dollars: a 4.11-rupee move to 80.00 earns USD 513,750, a 3.89-rupee move to 88.00 costs USD 442,045, because each rupee of difference is divided by a different fixing: USD 125,000 a rupee at 80.00 against USD 113,636 at 88.00. In rupees it is linear; it is the conversion that bends it. When the rupee weakens the company pays the bank, and that cash leaves on settlement date even though the cheaper rupee costs have not yet been paid, which is a liquidity point the budget should carry.
Dividing by the contract rate instead of the fixing. It gives 10,000,000 × 1.61 ÷ 84.11 = USD 191,416, USD 3,736 less than the correct figure, and the hedge then appears to leak: the net cost no longer comes back to exactly 10,000,000. Spreadsheets built for deliverable forwards often make this error when they are reused for NDFs. Check the confirmation as well: it names the fixing source and time (for the rupee, the FBIL reference rate), the fixing date and the settlement currency, and those three terms define the formula.
Basis risk sits in the fixing. The hedge is perfect only if the subsidiary's rupees are bought at the fixing. Buy them a week later at a different rate and the difference is unhedged, in either direction.
NDF settlement = notional × (contract − fixing) ÷ fixing, paid in dollars two days after the fixing. Here it is USD 195,152 to the company, which with the onshore purchase fixes the cost at USD 10,000,000. Before maturity, the same contract is marked to market like any forward, as in valuing an FX forward after spot moves, and the free workbook for this case sets out how a forward's cost, cash and collateral show up in a hedging programme.
The party the market moved against. A company that sold dollars forward at 84.11 receives dollars if the fixing comes in below the contract rate and pays if it comes in above. At a fixing of 86.00 on USD 10,000,000 it pays the bank USD 219,767, offset by cheaper rupees in the onshore market.
Because the gain or loss arises in the restricted currency and must be converted into dollars at a rate both parties observe at maturity. On USD 10,000,000 a move from 84.11 to 82.50 is worth INR 16.1m, and INR 16.1m divided by the 82.50 fixing is USD 195,152.
A deliverable forward exchanges both currencies in full at the contract rate. An NDF exchanges only the difference, in dollars, based on an official fixing. For a company buying its rupees at the fixing the economics are the same: in the example both lock the cost of INR 841.1m at USD 10,000,000.
This article is one calculation from Derivatives. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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