? Guide to Accrued Interest Calculation for Bonds

This document provides a high-level technical reference for implementing bond accrued interest calculations in PHP. It supports a variety of day count conventions and handles both fixed and floating rate instruments, including those based on risk-free rates (RFRs).

? Contents

1. Terminology
2. Accrued Interest Calculation Steps
3. Day Count Conventions
4. Actual/Actual (ICMA) Method
5. Floating Rate Notes Based on Risk-Free Rates

Terminology

• Accrued Interest: Interest accumulated from the last coupon payment to the settlement date.
• Settlement Date: The day a bond transaction is settled.
• Coupon Frequency: Number of coupon payments per year.
• Jouissance: First date of interest entitlement.
• D1.M1.Y1: Start date of interest period.
• D2.M2.Y2: End date (settlement or maturity).
• D3.M3.Y3: Next coupon payment date.

Accrued Interest Calculation Steps

1. Determine Settlement Date - Follows defined T+n cycles and skips currency holidays.
2. Define Accrued Interest Dates - Based on coupon schedules and settlement date.
3. Calculate Number of Interest-Bearing Days - Depends on the bond?s day count convention.
4. Compute Accrued Interest - Uses formulas specific to the selected day count method.

Day Count Conventions

| Method | Formula | |------------------------|------------------------------------------------| | 30/360 (ISDA/ICMA) | A = C * (N / 360) | | Actual/360 | A = C * (N / 360) | | Actual/365 (Fixed) | A = C * (N / 365) | | Actual/365L | A = C * (N / Y) (Y = days in year) | | Actual/Actual (ICMA) | A = (C / F) * (N / C) (regular coupons) | | Actual/364 | A = (C * (N / 364) |

Actual/Actual (ICMA) Method

• Differentiates regular vs irregular periods.
• Regular: Periods that are clean multiples of coupon frequency.
• Irregular: Uses notional coupon periods to adjust calculations.

• In irregular cases, the formula:
  A = ? [(CouponAmount / F) * (Ni / Ci)]
  

  where Ni = days in notional period i, Ci = length of notional period i.

Floating Rate Notes Based on Risk-Free Rates

With the shift from LIBOR to RFRs: - Interest is calculated in arrears, not forward-looking. - A lookback period defines how rates are compounded over time. - Key components: - Compounded rates with optional margin rate. - Modified Business Day Convention. - Rate flooring to prevent negative interest. - Custom lookback windows. - Rounded rates based on ISDA standards.

? Key Features for Implementation

• Support for multiple day count methods.
• Handling of regular and irregular coupon schedules.
• Floating rate notes using backward-looking compounded RFRs.
• Modular architecture to accommodate bond-specific parameters.

?? Recommended Use in PHP

Consider implementing the above logic as: - Bond class with properties for coupon, frequency, dates. - InterestCalculator class using strategy pattern for each day count convention. - Separate module for RFR-based FRN calculations.