Introduction

Understanding the nuances of bond pricing is fundamental in fixed income markets. Bond prices are often quoted as either “clean” or “dirty”. The distinction between these two terms is critical as it involves accrued interest. In this chapter, we will explore the concepts of clean and dirty bond pricing, elucidating the implications of accrued interest in bond valuation. We will employ an arbitrage argument to illustrate the significance of these distinctions and how they can be applied effectively in bond pricing.

Clean Vs Dirty Bond Pricing:

Clean Bond Price: The clean bond price, also known as the flat price, represents the price of a bond exclusive of any accrued interest. It reflects the price of the bond itself, ignoring any interest that has accumulated since the last coupon payment. The formula to calculate clean bond price is given below.

$$\text{Clean Bond Price}=\text{Quoted Bond Price}-\text{Accrued Interest}$$

Dirty Bond Price: The dirty bond price, also referred to as the full price, includes both the actual price of the bond and the accrued interest. It represents the total cost that an investor must pay to acquire the bond. The formula to calculate dirty bond price is given below.

$$\text{Dirty Bond Price}=\text{Quoted Bond Price}+\text{Accrued Interest}$$

Accrued Interest

Accrued interest refers to the interest that has accumulated on a bond since its last coupon payment. It is the compensation that the bondholder is entitled to for holding the bond during this period. Accrued interest is calculated based on the bond’s coupon rate, the number of days since the last coupon payment, and the day count convention used.

The formula for calculating accrued interest is as follows:

$$\text{Accrued Interest}=\text{Face Value}\times \text{Coupon Rate}\times \left(\frac{\text{Days Since Last Coupon}}{\text{Days in Coupon Period}}\right)$$

Implications of Accrued Interest

Accrued interest is essential for both buyers and sellers of bonds. Here are the implications:

• Buyer’s Perspective: When a buyer purchases a bond, they must pay the dirty price, which includes accrued interest. This ensures that the seller is compensated for the interest earned up to that point.

• Seller’s Perspective: A seller receives the dirty price when selling a bond. This ensures that they are fully compensated for the bond’s value and the interest accrued during their ownership.

Arbitrage Argument

The arbitrage argument comes into play when the clean and dirty prices deviate from each other. Arbitrageurs aim to profit from these deviations by exploiting price differences. For example, if the clean price is significantly lower than the dirty price for a bond, an arbitrageur might buy the bond at the clean price and then receive the accrued interest when the next coupon payment occurs, making a profit.

Application to Bond Pricing

Understanding clean and dirty pricing is crucial for bond traders and investors. It allows them to accurately assess the true cost or value of a bond when buying or selling in the secondary market. Additionally, it helps in comparing bonds with different coupon payment dates and frequencies.