Implied FX Swap Rates with Currency-Specific Day Counts
Summary
The document explains how to infer one currency’s interest rate from spot and forward FX rates when the other currency’s rate is known. It applies interest rate parity, adjusting each rate for its own day-count convention over the swap’s accrual period. The example uses a USD/HKD swap spanning 366 days: USD accrues on ACT/360 and HKD on ACT/365. Applying those fractions to the parity equation produces the quoted implied HKD rate of 0.8486%, resolving the discrepancy with a calculation that treats both rates as annualized over the same basis.
The example shows why a leap-year accrual period and different currency conventions can materially affect a derived rate. Its result depends on the stated conventions, dates, and quoted FX rates; the document does not investigate whether a cross-currency basis adjustment is needed in other market settings or establish the conventions for other currency pairs.
Key ideas
- Implied FX rates can be derived by rearranging interest rate parity.
- Apply each currency’s own day-count fraction to its interest rate.
- A 366-day accrual can produce different year fractions under ACT/360 and ACT/365.
- The inferred rate depends on the market conventions and inputs used.
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Full text
# Implied interest rate from FX swap
# Implied interest rate from FX swap
This is not homework. I am trying to calculate the implied interest rate of one currency (C2) using an FX swap and the interest rate of another currency (C1 - base). I have the following:
Spot: 7.7587 (C2 per unit C1) Buy Notional (spot) C1: 12,888,757.14 Sell Notional (spot) C2: 100,000,000.00
Start date: 6-May-13 End date: 7-May-14
Buy Notional (forward) C2: 100,000,000.00 Sell Notional (forward) C1: 12,905,390,58 Forward FX rate: 7.7487
I have a borrowing in C1 for 0.9650% for the year. Using interest rate parity: $$ F_0 = S_0 \frac{1+r_{C2}}{1+r_{C1}} $$ I solve for $ r_{C2} = 0.8349\%$. However, I am told that the right answer is $0.8486\%$. Which should be the implied interest rate in currency C1. Am I crazy or missing something?
Do I need to consider FX basis?
EDIT If I use ACT/360 for C1 and ACT/365 for C2 with $ACT=365$ I get actually pretty close $(0.8483\%)$. Is that it? Is the difference caused by daycount?
C1 is USD C2 is HKD (I believe these are the correct day-count convention based on a paper by UBS). Not sure where to find the "official" declaration.
## Answer by perry (score 9, accepted)
https://quant.stackexchange.com/a/9300
Because the day count of your inquired date is 366 days:
- Hkd daycount is act/365 therefore 366/365
- Usd daycount is act/360 therefore 366/360
$$ \frac{7.7487}{7.7587} = \frac{1+r_2(\frac{366}{365})}{1+0.00965×\frac{366}{360}} $$
Solving for $r_2 = 0.8486$.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.