using tick data for spot-vol correlations

Friends,If spot is up 1% and vol is up 1%, what delta lean do you need?Say you’re long 1,000 vega and vol is 40%. Vol ticks up 0.4 (1% relative move), so P&L is +$400. To stay flat, you need to lean short $400 / 1% = $40,000 of underlying.Compactly:delta lean = −vega × σ × β-$400 = -1000 x 40% x 1.0σ is the vol in percent and β is the relative or percent vol move per 1% spot move. (Note that short vega flips the sign.)I introduced this idea in embedding spot-vol correlation in option deltas. It’...