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Term Structure of Interest Rates

Term Structure of Interest Rates is a sample of the publications under Tutorials and part of the ongoing tutorial section under Valuation with a focus on Fixed Income securities.

Term structure of interest rates remains one of the most important tools in the bond market for pricing fixed income securities.  This educational note is a primer to have a better understanding on this subject.

The series on Term Structure of Interest Rates discusses the following topics


  • Bonds Simplified : A brief overview of bonds which a look at yield, YTM (Yield to Maturity), yield curve and various types of yield curve
  • Understanding price and yield relationship
  • Overview and valuation of zero coupon bonds and deriving theoretical spot rate curve from the par yield curve
  • Calculating price of the bonds using spot rates and YTM
  • Understanding forward rates, calculating forward rates and much more

In the parlance of bond valuation spot rates have the utmost role as determinants of building blocks of understanding the term structure of interest rates. The price of the bond is the present value of the cash flows. The cash flows of bonds can be considered zero-coupon bonds. Zero-coupon bonds are not coupon securities but pay interest in the form of discounting the issue price to the face value. The yields of these zero-coupon bonds are also known as spot rates. Spot rates are discount rates of a Single Future Cash Flow like a zero-coupon bond.1

To derive the spot rate of each treasury security of a particular time it is important to known the spot rate of each of these securities. Before we understand how to derive a theoretical spot rate curve, we delve into a few basics. 

A bond has a face value or par value and coupon paying securities are issued at the face value and begin trading. A bond has a term to maturity during which term the issuer (the originator of the bond) promises to fulfill the conditions of the obligations attached to the bond. These include paying a coupon rate i.e. interest on the face value of the bond to the bondholder. Government treasuries like the US pay semiannual rates of interest although types of interest payments vary. According to classification by Fabozzi bonds with maturity between 1 to 5 years are short-term securities although for the tutorial’s bonds with maturities 3 to 6 months will also be referred to as short term securities while medium term ranges from 5 to 12 years. Long term bonds are of duration 20 or 30 years but usually on the run US treasury securities i.e. treasury securities issued recently range from 2,5 and 10 in intermediate term to 30 years in the long term. In the fig, yield refers to the current yield of the bond.

On the run securities and selected off the run securities or/are used to derive a theoretical spot rate curve from par yield curve of securities through Bootstrapping. This technique will be explained today.

To know more about types of issuers, selected various kinds of bonds and much more refer to the tutorial on Global Bond. The educational module does not include bonds with embedded options which will be discussed at a later date.

Bonds are often quoted in term of its current yield and yield to maturity.  As bonds trade upon issuance, the yields of the bond change.  The yield of the bonds is inversely related to price of the bonds. The price of the bonds is the present value of all the cash flows discounted at either the spot rates of respective time periods or yield to maturity.

Left Pic: Middle Road OPC Pvt Ltd


To have a better understanding of present value valuation refer to the module on  Concept of Present and Future Value.

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