Cross Rates and Swap Points for the CTP Exam
Which four figures go into a cross rate, and where forward points really come from.
Interbank markets quote most currencies against the US dollar. When a customer wants euro against rupee, or yen against rupee, the dealer builds the rate from two dollar quotes. That derived rate is a cross rate. Its forward version needs swap points, which come from the interest rate gap between the two currencies.
Both are Module IV arithmetic in the Certified Treasury Professional (CTP) exam. The trap in each is picking the right side of each quote, so the bank never gives the customer a better rate than it can cover at.
You save ₹250
- Full-length mocks
- Chapter-wise practice
- Calculation practice
One payment, no subscription · Valid for 1 month
The Rule for Picking Sides
- 1
Write each quote as base / quote currency
EUR/USD 1.0850/1.0852 means USD 1.0850 to 1.0852 per euro. USD/INR 84.1000/84.1200 means ₹84.1000 to ₹84.1200 per dollar.
- 2
If the dollar is base in one and quote in the other, multiply
EUR/USD x USD/INR = EUR/INR. Bid x bid gives the cross bid; ask x ask gives the cross ask.
- 3
If the dollar is base in both, divide
USD/INR divided by USD/JPY = JPY/INR. The cross bid uses the bid on top and the ask below; the cross ask uses the ask on top and the bid below.
- 4
Check the spread widened
As a percentage of the rate, a cross rate's spread is wider than either leg's. If yours narrowed, a side is swapped.
Worked Example 1: EUR/INR (Multiply)
Illustrative: EUR/USD 1.0850/1.0852 and USD/INR 84.1000/84.1200.
Bank buys EUR (bid)
Working
1.0850 x 84.1000
EUR/INR
₹91.2485
Bank sells EUR (ask)
Working
1.0852 x 84.1200
EUR/INR
₹91.2870
| Side | Working | EUR/INR |
|---|---|---|
| Bank buys EUR (bid) | 1.0850 x 84.1000 | ₹91.2485 |
| Bank sells EUR (ask) | 1.0852 x 84.1200 | ₹91.2870 |
Worked Example 2: JPY/INR (Divide)
Illustrative: USD/JPY 150.20/150.25 and USD/INR 84.1000/84.1200. Yen is usually quoted per 100 units.
Bank buys JPY (bid)
Working
84.1000 / 150.25 x 100
₹ per 100 JPY
₹55.9734
Bank sells JPY (ask)
Working
84.1200 / 150.20 x 100
₹ per 100 JPY
₹56.0053
| Side | Working | ₹ per 100 JPY |
|---|---|---|
| Bank buys JPY (bid) | 84.1000 / 150.25 x 100 | ₹55.9734 |
| Bank sells JPY (ask) | 84.1200 / 150.20 x 100 | ₹56.0053 |
Where Swap Points Come From
Swap points (the forward margin) are the forward rate minus the spot rate, in units of 0.0001. They are set by the interest gap between the two currencies, not by a view on where the rate is going. With rupee rates above dollar rates, the dollar trades at a forward premium against the rupee.
Theoretical forward = spot x (1 + rupee rate x days / 365) / (1 + dollar rate x days / 360). Rupee money market interest is counted on 365 days and dollar money market interest on 360, so each leg uses its own basis.
Quote-reading sums in the real format. No signup.
Worked Example 3: 90-Day Swap Points
Illustrative: spot USD/INR 84.10, rupee interest 6.50%, dollar interest 4.50%, 90 days.
- 1
Rupee factor
1 + 0.065 x 90 / 365 = 1.016027.
- 2
Dollar factor
1 + 0.045 x 90 / 360 = 1.011250.
- 3
Forward rate
84.10 x 1.016027 / 1.011250 = ₹84.4973.
- 4
Swap points
84.4973 minus 84.10 = ₹0.3973, or 3973 points of premium.
- 5
Annualised premium
0.3973 / 84.10 x 365 / 90 x 100 = 1.92% a year, close to the 2% rate gap.
Worked Example 4: A Broken-Date Forward
Customers rarely want exactly one or two months. Dealers interpolate the points linearly by days. Illustrative: 1-month (31 days) 1200 points, 2-month (61 days) 2300 points; the customer wants 45 days.
Points per extra day
Working
(2300 minus 1200) / (61 minus 31)
Result
36.67 points a day
Days beyond 1 month
Working
45 minus 31
Result
14 days
45-day points
Working
1200 + 36.67 x 14
Result
1713 points
Outright (spot bid 84.1000)
Working
84.1000 + 0.1713
Result
₹84.2713
| Step | Working | Result |
|---|---|---|
| Points per extra day | (2300 minus 1200) / (61 minus 31) | 36.67 points a day |
| Days beyond 1 month | 45 minus 31 | 14 days |
| 45-day points | 1200 + 36.67 x 14 | 1713 points |
| Outright (spot bid 84.1000) | 84.1000 + 0.1713 | ₹84.2713 |
Swaps in the Forex Market
- FX swap
- A spot deal and an opposite forward deal for the same amount, done together. The price is the swap points.
- Buy/sell swap
- Buy the currency for the near date and sell it for the far date. RBI's USD/INR buy/sell swap auction works the other way round from the bank's side: the bank sells dollars to RBI and buys them back on the far date.
- Sell/buy swap
- Sell the currency near and buy it back far. A bank long in spot dollars but short in forward dollars uses this to close the gap between dates.
- Funding a rupee gap
- A bank with surplus dollars and a rupee shortfall can sell dollars spot and buy them forward, borrowing rupees at the cost of the swap points.
How the CTP Exam Tests This
- check_circleCross rate sides: which of the four figures go into the bid and the ask.
- check_circleMultiply or divide: decided by where the dollar sits in each quote.
- check_circlePoints from interest rates: the higher-interest currency is at a forward discount.
- check_circleBroken dates: linear interpolation between the two nearest standard periods.
- check_circleForward duration: under FEDAI rules a forward contract's period is counted from the spot value date, not the deal date.
FAQs
How do you calculate a cross rate from two quotes?expand_more
If the common currency is the base in one quote and the quote currency in the other, multiply bid by bid and ask by ask. If it is the base in both, divide, taking bid over ask for the cross bid and ask over bid for the cross ask.
What are swap points?expand_more
The forward rate minus the spot rate, quoted in points of 0.0001. They reflect the interest rate difference between the two currencies over the period.
Why do I use 360 days for the dollar and 365 for the rupee?expand_more
Each currency's money market has its own day count. Dollar deposits use actual/360 and rupee money market interest uses actual/365, so each leg of the parity formula uses its own basis.
How is a broken-date forward priced?expand_more
By linear interpolation of the swap points between the two standard dates either side, using the number of days.
Access exam-specific mock tests directly from your Android device.Next steps
- Options Basicsarrow_forward
- Forward Premium & Discountarrow_forward
- Day Count Conventionsarrow_forward
- Swaps & FRAsarrow_forward
- Syllabusarrow_forward
100 questions on the full CTP syllabus, timed and scored.