macrocephalopod

The chart shows ES futures volatility 2013-now measured using 24 hour periods starting/ending at the indicated time. If there was no time of day effect this would be a flat line, in reality the close-to-close return is two percentage points higher than e.g. the 1pm-to-1pm return

The reason is huge flows around the close that distort the price away from fair value *despite* the additional liquidity available at this time (e.g. market-on-close orders and yes, maybe even dealer option hedging....)

The dumbest possible model for this is to write the observed price P(t) as the sum of a fair price F(t) and a random noise E(t) that represents excess demand at the close on day t

This model predicts that the variance of close-to-close returns is larger than the variance of "fair value" returns by 2 * Var(E) -- if we assume the difference between the 1pm-1pm and close-close returns is entirely due to this effect (it's not) than it implies

that Var(E) = (0.17^2 - 0.15^2)/2, which is the same as saying that the daily standard deviation of E is ~35 basis points, which is absolutely huge (it's smaller than this in reality but still pretty big -- and potentially tradable?)