Variance Risk Premium in Nifty 50 Weekly Expiry Cycles: VIX Calibration Bias and Regime Dependence

This paper asks a simple question: does India VIX actually predict how much the Nifty 50 moves each week? Using 380 weekly expiry cycles from February 2019 to June 2026, I find that it does not, at least not accurately. Implied volatility overstates realized weekly moves in nearly three out of four cycles. The mean Variance Risk Premium (VRP), defined as the difference between implied and realized weekly volatility, is +0.70% per cycle (t = 8.40, p < 0.001). Beyond this central finding, I show that conditioning on volatility regimes derived from a pre-sample period (2011-2018) reveals meaningful structure. VIX retains some predictive power for move magnitude at the aggregate level (ρ = 0.228, p < 0.001), but this relationship breaks down entirely within the Low VIX regime. Only the High VIX regime produces realized volatility distributions that are statistically distinct from the other two regimes. Perhaps most interestingly, High VIX weeks show a significant upward directional bias of 62.6% (p = 0.021), a pattern consistent with fear-driven selloffs partially reversing before expiry. These findings hold when the COVID-19 period is excluded. Taken together, the results point to a structural and persistent VRP in Indian weekly equity market data.