Value-at-Risk Estimation and Backtesting Through Crises: Market Risk in the Indian Context

Value-at-Risk (VaR) sets trading limits, capital and exchange margins, and its accuracy matters most in a crisis. This paper reviews three empirical studies of VaR in Indian markets, covering the NIFTY 50 [1], government securities [2] and the S&P CNX 500 and INR/USD [3], and re-examines their published results. Recomputing the Kupiec statistics shows that Samanta et al. report χ²(2) tail probabilities for a χ²(1) test; corrected, simple historical simulation (HS) on 8.07% GS 2017 is rejected at 5% (p = 0.0234), although the tail-index model still ranks first. Sharma’s average annual penalties rest on an unstated rule that charges every yellow-zone year 0.625, and two of her equity averages break it. Re-estimating VaR in real time on NIFTY 50 data for 23 March 2020, when the index fell 12.98%, shows that the day’s loss was 4.21, 2.59 and 1.66 times the normal, HS and EWMA one-day 99% VaR. Over January 2020 to October 2021 (457 days), only a max(HS, EWMA) hybrid passed Kupiec’s test (p = 0.0659), and it stayed in the Basel yellow zone. The studies agree that returns are fat-tailed and that normal VaR understates risk at 99%, but none of the models came close to the size of the crash. With the RBI moving commercial banks to the Simplified Standardised Approach from 1 April 2027, the findings bear most on internal limits and exchange margining, where models should be validated over a stress period with duration or multi-lag independence tests as well as exception counts.