The group took on record the estimation and backtesting results provided by Prof. Varma (see Appendix 1) from his ongoing research work on value at risk calculations in Indian financial markets. The group, being satisfied with these backtesting results, recommends the following margin fixation methodology as the initial methodology for the purposes of 3.1.1 above.

1. The exponential moving average method would be used to obtain the volatility estimate every day. The estimate at the end of day t, s_t is estimated using the previous volatility estimate s_t-1 (as at the end of day t-1),and the return r_t observed in the futures market during day t.

(s_t)² = l (s_t-1)² + (1 - l ) (r_t)²

where l is a parameter which determines how rapidly volatility estimates change.

2. A value of 0.94 would be used for l .
3. The margins for 99% VAR would be based on three sigma limits.
4. For statistical reasons, return is defined as the logarithmic return

r_t = ln(I_t/I_t-1)
where I_t is the index futures price at time t.
5. Given this statistical definition, the plus/minus three sigma limits for a 99% VAR would specify the maximum/minimum likely logarithmic returns. To convert these into percentage margins, the logarithmic returns would have to be converted into percentage price changes by reversing the logarithmic transformation. Therefore the percentage margin on short positions would be equal to 100(exp(3s_t)-1) and the percentage margin on long positions would be equal to 100(1-exp(-3s_t)). This implies slightly larger margins on short positions than on long positions, but the difference is not significant except during periods of high volatility where the difference merely reflects the fact that the downside is limited (prices can at most fall to zero) while the upside is unlimited. The derivatives exchange/clearing corporation may, if it so chooses, simply apply the higher margin on both the buy and sell side.
6. To use the formula in (a) above on the first day of index futures trading would require a value of s_t-1 , the estimated volatility at the end of the day preceding the first day of index futures trading. This would be obtained as follows. (i) Calculate the standard deviation of returns in the cash index during the last one year. (ii) Set the volatility estimate at the beginning of that year equal to this average value. (iii) Move forward through the year, one day at a time, using the formula in (a) above to get the estimated volatility at the end of that day using cash index prices instead of index future prices. (iv) The estimated volatility by this method at the end of the day preceding the first day of index futures trading would be the value of s_t-1 to be used in formula in (a) above at the end of the first day of futures trading. Thereafter each day’s estimate s_t become the s_t-1 for the next day.
7. As a transitional measure, for the first six months of trading (until the futures market stabilises with a reasonable level of trading), a parallel estimation of volatility would be done using the cash index prices instead of the index futures prices and the higher of the two volatility measures would be used to set margins.
8. As a further transitional measure, for the first six months of trading (until the futures market stabilises with a reasonable level of trading), the initial margin shall not be less than 5%.