CCIL introduced a Zero Coupon Sovereign Rupee Yield Curve in September 2002 by following a parametric approach, based on Nelson & Siegel equation. The Nelson & Siegel equation is as under:

ß0 is the contribution of long term component
ß1 is the contribution of short term component
ß2 indicates the contribution of medium term component
t is the decay factor and m is the maturity
ß2 & t determine the shape of the curve

While the curve has been consistently showing better fit to the traded data as compared to other similar curves available in the public domain, the limitation that the Nelson & Siegel equation based curve can take only one hump has been observed to come in the way of developing a zero curve which represents zero coupon yields appropriately across the curve. CCIL therefore has now developed an alternate parametric model viz. Nelson-Siegel-Svensson yield curve which is based on 6 parameters instead of 4 as in Nelson-Siegel model.

where - are the additional parameters to incorporate an additional slope change and a additional hump. This curve is expected to provide a relatively better fit to the data due to its ability to accommodate 2 humps. [Paper detailing the relative performance is available under Discussion Forum – article “Paper on N-S-S Yield Curve” published in March’ 05.]

This form of the yield curve has been put to use by the Central Banks of some of the advanced countries and it also appears that considering the kind of twist now being seen in the yield curve, it may be worthwhile to develop an Indian Sovereign yield curve on the similar lines, which will have the ability to capture twists in a better manner.

Methodology

For generation of the yield curve, the trade data for Central Government Securities and T- bills conducted through / reported in RBI’s Negotiated Dealing System (NDS) and NDS-Order Matching (NDS-OM) is taken into consideration. The process followed is as under:

1. Trade data is subjected to a filtering process for removal of market outliers

2. Each traded security is broken down into its constituent cash flows

3. An optimisation process is run to minimise the sum of the square of price errors weighted with inverse of respective durations to arrive at the parameters for Nelson-Siegel-Svensson curve based Zero Coupon Yield Curve.

Assessment of Fit

The Analysis of the price error and per trade error reveals that the N-S-S model gives a considerably better fit as compared to than the N-S model. The N-S-S model gives a Per Trade Error of Re. 0.10 to Re. 0.50 while the N-S model had an error ranging between Re. 0.30 and Re. 1.00.

We also observed a better fit for the shorter to medium tenor zones in the N-S-S curve without loosing the fit for the longer tenors as is observed in the N-S model. The N-S-S was also found to provide a steepness in the Zero Curve for the shorter tenor points which was not attainable in the N-S model.

It therefore appears that N-S-S equation based ZCYC may provide a much better alternative for creating a yield curve in the current state of the market.

Release of NSS ZCYC Parameters

CCIL proposes to release these parameters now on a daily basis by about 7.15 PM. The information will be made available using an excel file which will show:

1. Price Error of the traded securities of the day

2. Comparison of the ZCYC Rates for two dates

3. Chart of comparison of the ZCYC of the two dates selected

CCIL seeks feedbacks and suggestions on the proposed methodology from market participants. Based on the feedback of the market participants, CCIL will consider adopting the N-S-S model of ZCYC for valuation and margining purposes.

[Disclaimer: CCIL takes due care and caution in compilation of data and compute various parameters/prices etc. and also takes reasonable care to make the data available in time. CCIL however does not guarantee accuracy, adequacy or completeness of data/prices/computation and is not responsible in any way for making the data/prices available on a regular basis or for any error or omission or for the results obtained from the use of such information.]