Development of a Rupee Yield Curve



CCIL Rupee Yield Curve

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Clearing Corporations the world over are entities which are like Nilkantha in the Indian Mythology. By becoming central counterparty to the trades done by its members, the Corporation absorbs an enormous amount of risk. It manages the risks through its risk management process in such a manner that the ultimate risk to its members from fails are reduced to the minimum.

For efficient risk management, the clearing corporation relies heavily on its valuation models and its risk measurement methodology. And for both of these, yield curve serves as the backbone.

The Clearing Corporation of India Ltd. (CCIL) came into existence with the mandate of offering Guaranteed Settlement for trades in Indian Government Securities. Hence, the search for a proper Rupee Yield Curve started almost from its inception.

Indian money market is essentially an overnight market. Although, some transactions do occur in term funds/Overnight Indexed Rate Swaps (OIRS), the rates are neither representative nor readily available. One redeeming feature, however, is the ready availability of data regarding trades in Government Securities which Reserve Bank of India have been making available through its website for the last six years or so.

Market participants consulted gave us valuable insights into the complexities involved in developing a properly functioning Yield Curve. A section of the market held that as the market still trades mostly on Yield to Maturity (YTM), CCIL could consider having an YTM based valuation methodology.

At CCIL, we examined the issues in the light of CCIL’s long term objective of being a vehicle for effective risk mitigation for the market participants. It was felt that an YTM based Yield Curve and valuation based on such curve would not be fair due to the extent of inaccuracies introduced by YTM based computations. Another issue that we had to grapple with at this stage was compounding of interest with different basis. A close look revealed that the impact of different basis of compounding on valuation also would be significant. As a result, we finally zeroed on Zero Coupon Yield Curve as against YTM curve and continuous compounding as against discrete compounding as the starting point.

The choice then was between Boot strapped yield curve or an yield curve based on some parametric approach like Nelson & Siegel equation or Svensson’s equation. Boot strapped curve is very popular in the international market. It involves step by step estimation of interest rates using observed prices (of pre-selected highly liquid bonds or other instruments ). However, in the Indian market, lack of market data spread across all maturities came in the way of development of a stable curve through this process. Typically, in Indian market volumes are concentrated in mid-term maturity of around 9 -15 years, with 6-8 securities accounting for nearly 60-70% of the total market volumes.

Given this situation, a parametric approach to estimate the term structure of interest rate was found to be the only practical solution. It was found to be more suitable due to the operational ease in regard to the generation of fairly representative yield curve with sparse data. We tested models based on both Nelson & Siegel equation and Svensson’s equation (an extended version of Nelson & Siegel equation which can accommodate two humps and is widely used in the developed countries). Our experiment however showed that for the data in the Indian market, Svensson’s equation based yield curves were not significantly better than the yield curves based on Nelson & Siegel equation. Further, estimation of six parameters of Svensson’s equation introduced much more complexities into the calculations as compared to the estimation of four parameters of Nelson & Siegel equation.

Nelson & Siegel equation which denotes the yield curve is as follows:

Spot Rate = β0 + (β1+β2) * [(1-exp (-m/τ )] )]/(m/τ) – β2*exp (-m/τ )

where

β0 is the contribution of long term component

β1 is the contribution of short term component

β2 indicates the contribution of medium term component

τ is the decay factor

m is the maturity

β2 & τ determine the shape of the curve

Generation of an yield curve based on this equation at CCIL involves estimation of values of βs and τ in such a manner that the difference between the prices of the securities computed using these parameters (by way of aggregating all cash flows of a bond after appropriate discounting) and the market prices of the respective securities are kept at the minimum. In reality, the aggregate of square of price errors multiplied by the respective inverse of durations is minimised.

CCIL has a fairly representative database to work on as by now almost all deals are settled over the NDS / CCIL route. This data is further filtered by a process of identifying and eliminating small value deals and price outliers. Further,, trade data in respect of Central Govt. securities and T bills are only taken into consideration so that the underlying prices are not unduly influenced by the credit quality of the issuers. While doing the estimation of the parameters, it is also ensured that yields do not turn negative at any point of time and represent actual market conditions. This adjustment sometime becomes necessary due to non-availability of prices across all maturities.

The yield curve generation process followed by us has been subjected to rigorous testing. Its sustainability under volatile market conditions has been analysed by generating yield curves for the most volatile days over the past two years. The price errors (i.e. the difference between the traded price & the theoretical price for a security) at our end were found to be in the range of rupees 0-2 (at times price errors of around Rs.3/- observed in case of long term illiquid securities), while in terms of average of square of price errors per trade, it worked out to be in the range of 0.35 paisa to 0.75 paisa, which was within the tolerance level for Indian markets. [The yield error tolerance limit for Indian market is generally believed at a higher level of around 10-15 basis points, as compared to those for US & Japan market which are at around 5-7 basis points and 9-10 basis points respectively].

The generation of CCIL yield curve has been a significant milestone. As mentioned in the beginning, Indian market as yet do not have adequate liquidity and depth across all maturities. We hope that introduction of CBLO by CCIL would address this issue as far as the lower end of the yield curve is concerned. Introduction of STRIPS in the near future should also provide depth to the market across the maturities. Moreover, preference for higher coupon securities by a segment of the market and relative illiquidity in case of some securities also introduces some amount of inconsistency in yield expectations. For generation of a more refined yield curve it is essential to capture the impact of these factors appropriately, and we are working towards this. We expect that as the depth in the market increases, we would be in a position to generate an yield curve which will represent the normal yield expectations of the market in an even more appropriate manner.

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