Interest Calculation Rules

Access the Mathema Options Pricing System, which supports foreign exchange options and structured product pricing and valuation!

The following is a detailed explanation of the above interest calculation rules. These Day Count Conventions determine how to calculate the length of time between two dates (usually in years) and are used for calculating interest on financial instruments. These rules are widely applied in financial instruments such as interest rate derivatives, bonds, and loans.

1. Actual/360

Rules：
- The number of interest calculation days is the actual number of days。
- Assuming there are 360 days per year
- Calculation formula：Day Count Fraction = Actual Days / 360。
Features：
- The interest calculation is based on the actual number of days, but the year is fixed at 360 days instead of the actual 365 or 366 days.
- Commonly used for short-term money market instruments (e.g., deposits, loans) and foreign exchange transactions.
Impact：
- Interest is typically slightly lower because the year is shortened to 360 days.
Applications：
- Euro money markets, US dollar money markets, and foreign exchange forwards (FX Forwards).

2. Actual/365 Fixed

Rules：
- The interest calculation is based on the actual number of days (Actual Days).。
- Assumes a year has 365 days, regardless of whether it is a leap year.
- Calculation formula：Day Count Fraction = Actual Days / 365.
Features：
- Fixed at 365 days per year, without distinguishing between common years and leap years.
- Commonly used in the GBP money market and bond markets.
Impact：
- Interest is typically slightly higher than Act/360 because the year is longer by 5 days.
应用：
- GBP money market.

3. 30E/360 (Eurobond Basis or 30/360 ISDA)

Rules
- Each month is fixed at 30 days, and each year is fixed at 12 months, totaling 360 days.
- Handling Rules：
  - If the 31st day of a month is involved in the calculation, it is treated as the 30th day of that month.
  - If the start date is the 31st, it is adjusted to the 30th.
- Calculation formula：Day Count Fraction = ((End Year - Start Year) * 360 + (End Month - Start Month) * 30 + (End Day - Start Day)) / 360。
Features：
- Assumes each month has only 30 days, simplifying calculations.
- Commonly used in the European bond market and fixed-rate bonds.
Impact：
- Simplifies interest calculations and is widely applicable.
Applications：
- European bond market, ISDA standard agreements.

4. 30E/360 ISDA (30E/360 International Standard)

Rules:
- Similar to 30E/360, but with slight differences in handling dates:
  - If the start date is the 31st, it is adjusted to the 30th.
  - 如果结束日是 31 日，且起始日是当月的 30 日或 31 日，则结束日调整为 30 日。If the end date is the 31st, and the start date is the 30th or 31st of the month, the end date is adjusted to the 30th.
- Other rules are the same as 30E/360.
Features：
- This is the standard defined by the International Swaps and Derivatives Association (ISDA).
Impact:
- Differences from 30E/360 are minimal but may result in slight variations in calculation results.
Applications:
- Derivative transactions under ISDA standard agreements.

5. 30E+/360 (30E+/360)

Rules:
- Similar to 30E/360, but with an additional rule:
  - If the end date is the 31st, it is adjusted to the 1st of the next month.
- Other rules are the same as 30E/360.
Features:
- Adjusts the end date to the next month when it is the 31st, further simplifying calculations.
Impact:
- Adjusted date handling may result in slightly different interest outcomes.
Applications：
- Certain specific bonds and derivatives.

6. 30U/360 (30/360 US or Bond Basis)

Rules:
- Each month is fixed at 30 days, and each year is fixed at 360 days.
- Handling Rules
  - If the start date is the 31st, it is adjusted to the 30th of the same month.
  - If the end date is the 31st, it remains unchanged.
- The calculation formula is similar to 30E/360, but the date handling rules differ.
Features:
- This is the standard interest calculation method in the US market.
Impact：
- Differences from 30E/360 lie only in the date handling rules.
应用：
- US bond market.

7. Act/Act ISDA (Actual/Actual ISDA)

Rules:
- Based on the actual number of days and the actual number of days in the year (365 days for common years, 366 days for leap years).
- Calculation formula:
  - Day Count Fraction = Actual Days / Days in the Year。
Features:
- Precisely accounts for actual days, suitable for complex interest calculations.
Impact:
- Most accurate but computationally complex.
Applications:
- Derivative transactions under ISDA agreements.

8. Act/Act ICMA (Actual/Actual ICMA)

Rules:
- Similar to Act/Act ISDA but used for bond coupon payments.
- Calculation formula：
  - Day Count Fraction = ((Actual Days / Coupon Period Days) * (Number of Coupon Periods))
Features:
- Specifically designed for the bond market, considering the frequency of coupon payments.
Impact:
- Suitable for bonds with periodic coupon payments.
Applications:
- Bond market.

9. Act/365L (Actual/365 Leap)

Rules:
- Based on the actual number of days, but leap years are calculated with 366 days.
- Calculation formula：
  - Day Count Fraction = Actual Days / (365 or 366)。
Features：
- Combines features of Act/365 Fixed and Act/Act。
Impact：
- More accurately reflects the impact of leap years.
Applications:
- Certain specific money markets and derivative markets.

10. Act/Act AFB (Actual/Actual Association Française de Banques)

Rules:
- Similar to Act/Act ISDA but with slight differences:
  - Divides the interest period into parts across different years, calculating the proportion of days in each year separately.
- Calculation formula:：
  - Day Count Fraction = (Actual Days / Days in the Current Year) + (Actual Days / Days in the Next Year)。
Features:
- Specifically used in the French market.
Impact:
- Precise but more complex to calculate.
Applications:
- French bond market.

11. Act/365 Leap

Rules:
- Similar to Act/365 Fixed but considers 366 days in leap years.
- Calculation formula:
  - Day Count Fraction = Actual Days / (365 or 366)。
Features:
- Combines features of Act/365 Fixed and Act/Act.
Impact:
- Higher interest rates in leap years.
Applications:
- Specific markets.

12. Act/Act XTR

Rules:
- A special variant of Act/Act, typically used in complex financial instruments.
- Specific rules may vary depending on the market or agreement.

13. Act/Act ICMA Complement

Rules:
- Complementary rules to the ICMA version, used in specific cases for bond coupon payments.
Features:
- Used only when Act/Act ICMA is not applicable.
Applications:
- Bond market.

14. Act/252

Rules:
- Interest calculation is based on the actual number of days.
- Assumes 252 days per year (typically the number of trading days).
- Calculation formula：Day Count Fraction = Actual Days / 252。
Features:
- Specifically designed for equity and futures markets, based on the number of trading days per year.
Impact:
- Interest calculations are closely tied to market trading days.
Applications:
- Equity index futures, foreign exchange markets.

Summary

These day count conventions are applied in different markets and financial instruments. Choosing the appropriate convention depends on the following factors:

Market Standards: Different markets and instruments have their own conventions (e.g., 30E/360 for the Eurobond market, 30U/360 for the US market).
Interest Precision： Conventions like Act/Act ISDA are more precise but computationally complex.
Cost Impact： Act/360 typically results in lower interest, while Act/365 Fixed results in higher interest.

In practice, the choice of day count convention depends on the transaction agreement, market practices, and the characteristics of the financial instrument.

Reference《 CFETS Product Guide V4.2》！