Gap fills

Nifty gaps up 0.8% and the trailing intraday volatility is 0.7%. (a) Under Proposition 4A.4, compute the probability that the gap is filled and the probability that the day closes below the previous close. (b) Compare (a) with the empirical fill rate in the 1.0–1.5 bucket of Worked example 4A.3, and recompute the fill probability with intraday volatility 1.3 times the trailing estimate. (c) A trader claims "gaps above 0.5% fill 35% of the time on Nifty, so fading them is profitable." Explain what is missing from the argument.