Matrix pricing of bonds is an estimation technique used to estimate the market price of securities that are not actively traded. Matrix pricing is primarily used in fixed income, to estimate the price of bonds that do not have an active market. The price of the bond is estimated by comparing it to corporate bonds with an active market, and that have similar maturities, coupon rates, and credit rating. This relative estimation process can be very helpful for debt valuation of private companies, which typically don’t report as much information as public companies.
Another use of matrix pricing is for bond underwriting, which can be used to estimate what the market’s required rate of return on the bond will be.
Comparable bonds matrix pricing valuation model
For example consider a 3years, 4% semiannual bond X that has to be valued for yearend reporting. Comparable bonds whose prices are known are summarised in the matrix below (example calculation YTM – 2years in #2 below). Based on these four bonds, the fair value of the bond X can be determined.
Table for matrix pricing – Comparables 

2% coupon 
3% coupon 
4% coupon 
5% coupon 

2years 
98.500 
102.250 

YTM – 2years 
3.786% 
3.821% 

3years 
Bond X 

4years 

5years 
90.250 
99.125 

YTM – 5years 
4.181% 
4.196% 
In 6 steps the fair value of bond X is determined using the matrix pricing method.
1. Select comparable bonds
See table above, it was not possible to find similar bonds with the 3years maturity. Instead, two 2years bonds and two 5years bonds were selected, that more closely matched the characteristics of bond X.
2. Determine the yield to maturity (YTM) of comparable bonds in an active relevant market
Calculationexplanation: https://www.investopedia.com/terms/y/yieldtomaturity.asp
For the 3% comparable bond, the YTM of a twoyear, 3% coupon is:
Current price = 98.5
Par value = 100
Years to maturity = 2 years
Annual coupon rate in % = 3.00%, paid semiannual
The resulting yield to maturity is: 3.786%
Used the calculator on: https://dqydj.com/bondyieldtomaturitycalculator/
3. Determine the average yield for 2years bonds
(3.786% + 3.821%) / 2 = 3.8035% or 3.80%
4. Determine the average yield for 5years bonds
(4.181% + 4.196%) / 2 = 4.1885% or 4.19%
5. Determine the 3years yield using linear interpolation
x can be calculated as follows:
3years (Bond X) – 2years (reference)
⸺⸺⸺⸺⸺⸺⸺⸺⸺⸺⸺ x (5years average yield (reference) – 3years average yield (reference)) =
5years (reference) – 2years (reference)
[(3 – 2) / ( 5 2 )] x (4.19% – 3.80%) = 0.1283% or 0.13%, 3.80% + 0.13% = 3.93%
6. Using the 3years yield the price of the 3years bond is 100.2
Given an estimated yieldtomaturity of 3.93%, the estimated price of the 3year, 4% semiannual bond X, that is illiquid 100.2 per 100 of each par value. To find this value, we need to plug in the following variables into the financial calculator: N=6; I/Y=1.966; PMT=2; FV=100; CPT => PV = 100.1906
Points for consideration using the matrix pricing method:
 Matrix pricing is primarily used when underwriting new bonds to estimate the required yield spread over the benchmark rate
 Benchmark rate is a widely used market rate for example LIBOR, or a government bond with the same maturity as the bond being priced
 assume the YTM for a new bond is calculated using the matrix pricing method a 2.2% and a comparable government bond has a yield of 2.0%. The difference of 0.2% is called the required yield spread or spread over the benchmark
 Yield spreads are always specified in basis points where I basis point is onehunderdth of a percentage point. In this case 0.2% is 20 basis points.
Matrix pricing is an estimation technique used to estimate
Matrix pricing is an estimation technique used to estimate Matrix pricing is an estimation technique used to estimate Matrix pricing is an estimation technique used to estimate.
Matrix pricing
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