Delta Hedge Calculator (Shares to Hedge, Rebalancing & Gamma P&L)

How it works

net delta = contracts × 100 × option delta + shares · hedge = −net delta shares · after a move: new delta from the model → rebalance = −(new net delta) · hedged P&L ≈ ½ Γ (ΔS)² + θ Δt · expected daily edge = ½ Γ S² (σ²_realised − σ²_implied) ÷ 252

An option's delta says how many shares it behaves like at this moment, so holding the opposite number of shares makes a position indifferent to small moves — but only for a moment, because delta itself changes with the price at the rate given by gamma, and the hedge must be adjusted as the underlying travels. Doing so systematically turns the position into a bet on movement itself: the long-option hedger buys low and sells high as they rebalance and profits when the stock moves more than the implied volatility priced in, paying theta for the privilege, while the short-option hedger earns theta and pays out on big moves. The classic result that the edge is proportional to gamma times the difference of realised and implied variance falls straight out of that mechanism.

Worked example

Short 20 calls struck at $155 on a $150 stock with 40 days left at 30% volatility: each call has a delta of 0.41, so the book is short 817 deltas and is flattened by buying 817 shares (about $122,600). After a 3% rally to $154.50 the delta rises to 0.53 and another 236 shares must be bought; the hedged book loses about $530 on the move (short gamma of −52), while it earns about $160 a day of theta when the stock sits still. If realised volatility comes in at 24% against 30% implied, the expected edge is roughly $75 a day.

Frequently asked questions