Fixed income instruments (FII) can be categorized by

type of payments. A periodic interest payment is paid by many fixed income

instruments to the holder, and an amount due at maturity, the redemption value.

Some instruments pay the principal amount together with the entire outstanding

amount of interest on the instrument as a lump sum amount at maturity. These

instruments are known as ‘zero coupon’ instruments (Eg: Treasury Bills).

A zero coupon bond is defined as “a debt

security that does not pay back an interest (a coupon)”. But it is traded in a

stock exchange at a greater discount, generating profits at the maturity when

the bond is redeemed for its full face value. Others are bonds that are

stripped off their coupons by a financial institution and resold as a zero

coupon bond. The entire payment including the coupon at the time of maturity is

offered later. The price of zero coupon bonds have a tendency to fluctuate more

than the prices of coupon bonds (Momoh,

2018).

Yield curve is obtained by plotting the

interest rates obtained from the securities against the time (monthly, daily or

annually) for securities having different maturity dates. These plotted data

have been used in various studies to identify behavior of the securities and to

predict the future behaviors. Various studies have been conducted to

investigate the behavior of various types of treasury bonds and bills by using

the yield curve.

The return on capital

invested in fixed income earning securities is commonly called as yield. The

yield on any instrument has two distinct aspects, a regular income in the form

of interest income (coupon payments) and changes in the market value and the

fixed income gearing securities (Thomas et al.).

Durbha, Datta Roy and

Pawaskar in their paper titled “Estimating the Zero Coupon Yield Curve” have

pointed out factors the Maturity period, Coupon rate, Tax rate, Marketability

and Risk factor, which make a yield differential among the fixed income bearing

securities. Further they have pointed out that the government securities which

are considered as the safest securities to invest also carries hidden risks as Purchasing

power risk and Interest rate risks.

According to the authors

the behavior of inflation within the country arises due to the purchasing power

risk and lead to changes in real rate of return. Interest rate risk is produced

due to the oscillations in prices of the securities. In such a case the

investors should regulate their portfolios accordingly.

Numerous

contributions in finance have proved that imposing no-arbitrage constraints in

empirical models of the yield curve improve their empirical features. The

additional features time-varying parameters, time-varying variances of

structural shocks, flexible pricing kernels, additional shocks and latent

variables have brought model implied yields and experimental yields closer

together (Graeve, et al). Both the short term interest rate and the term spread

have an impressive record in predicting GDP growth (Estrella 2005, Ang et al.

2006,).

1.1. Motivation behind the Use

of Zero Coupon Yield Curve for Valuation of Fixed Income Instruments

Modeled as a series of cash flows due at dissimilar

points of time in the future, the causal price of a fixed income instrument can

be calculated as the net present value of the stream of cash flows. Each cash

flow has to be discounted using the interest rate for the related term to

maturity. The appropriate spot rates to be used for this purpose are provided

by the Zero Coupon Yield Curve

(Thomas, et.al.). The equation

used is given below.

C = coupon

R = redemption amount

m = time to maturity

1.2. The uses of estimating a term structure

Once an estimate of the term structure based on

default-free government securities is obtained, it can be used to price all

fixed income instruments after adding an appropriate credit spread. It can be

used to value government securities that do not trade on a given day, or to

provide default-free valuations for corporate bonds. Estimates of the Zero Coupon Yield Curve

at regular intervals over a period of time provides us with a time-series of

the interest rate structure in the economy, which can be used to analyze the

extent of impact of monetary policy. This also forms an input for VaR systems

for fixed income systems and portfolios.

1.3.

The inflation and the real economic activity were empirically

predicted by the slope of the yield curve. There is no standard theory for this

relationship. The model in this paper suggests that the relationships are not

structural but are instead influenced by the monetary policy regime.

Even though theoretical

foundation for the statistical proof with regard to both output and inflation

is limited, there are studies done separately.