Day-Count Conventions

Day-count conventions determine the fraction of a year ($\tau$) between two dates $d_1$ and $d_2$, governing interest accrual and discount factors:

$\tau(d_1, d_2) = \frac{\text{Days}(d_1, d_2)}{\text{YearBase}}$

Supported Conventions

1. Actual/Actual ICMA (Bond Standard)

Used for sovereign and corporate bonds. Calculates accrual relative to the actual number of days in the current coupon period:

$\tau(d_1, d_2) = \frac{d_2 - d_1}{f \cdot (p_2 - p_1)}$

where $f$ is the payment frequency and $[p_1, p_2]$ is the reference coupon period.

2. Actual/Actual ISDA (Swap Standard)

Splits calculation across calendar years:

$\tau(d_1, d_2) = \frac{\text{Days in Year}_1}{\text{Days in Year}_1 \text{ (365 or 366)}} + \frac{\text{Days in Year}_2}{\text{Days in Year}_2 \text{ (365 or 366)}}$

3. Actual/360 & Actual/365 Fixed

• Actual/360: Standard in money markets (US Treasury bills, commercial paper, SOFR/Euribor loans): $\tau(d_1, d_2) = \frac{d_2 - d_1}{360}$
• Actual/365 Fixed: Standard in UK, Commonwealth, and JPY markets: $\tau(d_1, d_2) = \frac{d_2 - d_1}{365}$

4. 30/360 Family (US & Eurobond)

Treats all full months as 30 days and a year as 360 days:

$\text{Days} = 360(Y_2 - Y_1) + 30(M_2 - M_1) + (D_2 - D_1)$

• 30/360 US (Bond Basis): Adjusts $D_1$ and $D_2$ based on end-of-month and February rules.
• 30E/360 (Eurobond Basis): If $D_1 = 31 \Rightarrow D_1 = 30$; if $D_2 = 31 \Rightarrow D_2 = 30$.

5. Business/252

Used primarily in Brazilian and Latin American fixed income:

$\tau(d_1, d_2) = \frac{\text{BusinessDays}(d_1, d_2, \text{Calendar})}{252}$

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Rust Code Example

use sabiquant::core::Date;
use sabiquant::core::daycount::{
    DayCounter, ActualActualICMA, ActualActualISDA, Actual360, Actual365Fixed, Thirty360US
};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let d1 = Date::from_ymd(2024, 2, 1)?; // Leap year
    let d2 = Date::from_ymd(2024, 8, 1)?;

    let act_360 = Actual360::default();
    let act_365 = Actual365Fixed::default();
    let thirty_360 = Thirty360US::default();
    let isda = ActualActualISDA::default();

    println!("Actual/360:     {:.6}", act_360.year_fraction(d1, d2)?);
    println!("Actual/365:     {:.6}", act_365.year_fraction(d1, d2)?);
    println!("30/360 US:      {:.6}", thirty_360.year_fraction(d1, d2)?);
    println!("Act/Act ISDA:   {:.6}", isda.year_fraction(d1, d2)?);

    Ok(())
}