The Committee for the Development of the Debt Market studied various alternative methodologies, which could be used for compiling a true reference rate in the market. This market is characterised by limited number of participants, who at times, take a unidirectional view of the market. Some of the methodologies studied by the committee are as under:

Volume weighted average (VWA) is calculated by averaging the reported trades after weighting them with their respective volume. The VWA needs price volume data of all executed deals and is a reliable measure of the market sentiment. However the calculation of VWA has some constraints in the Indian context, as most participants prefer to keep their transactions confidential. Moreover, this method can give results only at the close of the market and therefore tends to give post-facto information and cannot be used to gauge the market mood at a point of time.

Polling (Delphic oracle) is used for obtaining reference rates by polling a few market participants and summarizing the prices they report. The highly liquid CME Eurodollar contract uses this method for its futures contract. The procedure involves querying bid and offer prices from eight market participants.

The basic question that is asked about this approach is, what motivates the respondents to report accurately? It is hard to design an incentive structure whereby the respondent does participate, and produces an accurate information. Full transparency would clearly help- if all eight quotes along with the name of the respondents are reported through a transparent medium, it would generate pressure to report fair prices. At the same time, this degree of public visibility might deter some players from participating. This is particularly a problem in an illiquid market, where various participants could have genuine or selfish reasons for reporting widely differing rates. Dealers have an incentive to falsify the reported rates to inject noise into the decision making of the market participants who use the reported reference rate or to gain from positions on derivative contracts which calculate payoffs using the reference rate.

Identifying and isolating noise in data: Having selected an appropriate technique for collecting data, one has to devise methods to identify and isolate the noise in data so as to minimise the impact of the extreme values on the final result, i.e. the reference rate. The most commonly used methods for this purpose are discussed hereunder:

Traded mean: Calculating fixed trimmed mean of the reported rates have been used by some organizations which need to use a reference rate, e.g. the CME for its Eurodollars contract, the CBOT for its Municipal Bond Index, etc. They collect rates from individual dealers and compute a reference rate as the trimmed mean is obtained after deleting "n" highest and lowest observations. For example, at CME Eurodollar, the two highest and two lowest quotes are rejected and the rest of the quotes averaged to get a reference rate.

The major concerns in such a trimming procedure are vulnerability to market manipulation of the rates and the amount of sampling noise. Secondly, excessive trimming may lead to loss of information, whereas too little trimming may lead to excessive influence of the extreme values on the reference rate. Thirdly, the sample sizes are typically very small and hence statistics based on the assumptions of normal distribution give wrong inferences.

Bootstrapping: The bootstrap technique is a non-parametric method for computing the test statistics, i.e.

(i) Computing the reference rate as an average of the polled rates after an appropriate amount of trimming to minimise noise.

(ii) Computing a measure of dispersion i.e. the confidence intervals for the trimmed means.

In order to arrive at an efficient estimate of the reference rate, from the bid and offer rates collected from a known sample of dealers, the outliers or extreme values are identified. This is required so that the reference rate, which is a mean of the polled rates, is not unduly influenced by extreme observations, which are likely to be noisy.

A user is also interested in knowing the efficiency of this mean value. That is to say, he is interested in knowing the probability that the estimated trimmed mean lies in a given range. Thus, the standard deviation of the mean has to be estimated. Since the call market is heterogeneous, constrained by limited participants and dealers, the underlying distribution of the offer and bid rates is not normal and hence the usual measures of efficiency of the mean rate, i.e. the standard deviation, is not valid.

The bootstrap method does not make any assumptions about the distribution from which the trimmed mean is drawn. The bootstrap method facilitates construction of the entire distribution for the mean and hence all the required parameters can be calculated from this constructed distribution.

Since the observations are drawn at random and the number of simulations is very high, the probability of any extreme observations affecting the mean value and its standard deviation is extremely minimal.

The procedure for choosing an adaptive 'n' as opposed to using a fixed 'n' allows for reduction of sampling noise and hence makes the estimated mean more efficient.

As discussed above, the "Polling" with "Bootstrapping" scores over the other alternatives to collect data in a limited data set and to isolate the extreme values. FIMMDA-NSE MIBID/MIBOR therefore, uses polling to collect data from the market participants. While the quotes for the overnight money are polled between 0940- 0945 hours, quotes for the other terms are polled between 1130- 1140 hours to capture the market sentiment in a short interval of time. Thereafter, the data so collected is subjected to bootstrapping to identify the extreme values.

The bootstrapping technique involves generating multiple data sets based on the rates polled, wherein the number of iterations required is determined dynamically and could be as high as 10,000. Based on the means generated from these multiple data samples, the standard deviation is calculated. The bootstrapping technique is also used to identify the outliers in the polled data. This is done by trimming the data set of its extreme values and again using a bootstrapped sample to calculate the standard deviation. Bootstrapping ensures that the data sets are drawn at random and this guards against the possibility of cartelisation and of extreme observations influencing the mean. The mean corresponding to the lowest standard deviation is finally reported by ensuring acceptability of at least 14 observations each for bid and offers. The standard deviations associated with FIMMDA-NSE MIBID/MIBOR are also reported to help the market in assessing the distribution of rates.

Thus, the methodology adopted by FIMMDA-NSE MIBID/MIBOR not only seeks to tackle the limitation of the polling method but also uses adaptive trimming to identify and isolate the extreme value to derive a true representative benchmark for the market. Moreover, the entire process of polling and processing of data is completed in a time-bound schedule and the reference rates are released to the market every day.