Matrix pricing 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.

For example consider a 3-years, 4% semi-annual bond X that has to be valued for year-end reporting. Comparable bonds whose prices are known are summarised in the matrix below (example calculation YTM – 2-years in #2 below). Based on these four bonds, the fair value of the bond X can be determined.

| ||||

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

2-years | 98.500 | 102.250 | ||

YTM – 2-years | 3.786% | 3.821% | ||

3-years | Bond X | |||

4-years | ||||

5-years | 90.250 | 99.125 | ||

YTM – 5-years | 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 3-years maturity. Instead, two 2-years bonds and two 5-years 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**

Calculation-explanation: https://www.investopedia.com/terms/y/yieldtomaturity.asp

For the 3% comparable bond, the YTM of a two-year, 3% coupon is:

Current price = 98.5

Par value = 100

Years to maturity = 2 years

Annual coupon rate in % = 3.00%, paid semi-annual

The resulting yield to maturity is: 3.786%

Used the calculator on: https://dqydj.com/bond-yield-to-maturity-calculator/

**3. Determine the average yield for 2-years bonds**

(3.786% + 3.821%) / 2 = 3.8035% or 3.80%

**4. Determine the average yield for 5-years bonds**

(4.181% + 4.196%) / 2 = 4.1885% or 4.19%

**5. Determine the 3-years yield using linear interpolation**

x can be calculated as follows:

**3-years (Bond X) – 2-years (reference) **

**⸺⸺⸺⸺⸺⸺⸺⸺⸺⸺⸺ x (5-years average yield (reference) – 3-years average yield (reference)) =**

**5-years (reference) – 2-years (reference)**

[(3 – 2) / ( 5 -2 )] x (4.19% – 3.80%) = 0.1283% or 0.13%, 3.80% + 0.13% = 3.93%

**6. Using the 3-years yield the price of the 3-years bond is 100.2**

Given an estimated yield-to-maturity of 3.93%, the estimated price of the 3-year, 4% semi-annual 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 one-hunderdth 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