Delta Hedging Calculator

What Is Delta Hedging?

Delta hedging is a strategy that reduces or eliminates the directional risk of an options position by taking an offsetting position in the underlying stock. You compute the option’s delta (its sensitivity to stock price changes) and buy or sell shares to make the combined position delta-neutral — insensitive to small moves in the stock price.

Delta hedging is most commonly used by option sellers (market makers, premium sellers) who want to isolate their exposure to time decay and volatility without taking a directional bet on the stock. The hedge must be periodically rebalanced as delta changes with the stock price.

How Delta & Gamma Work

Delta (Δ) measures how much the option price changes for a $1 move in the stock. Call deltas range from 0 to +1; put deltas range from −1 to 0. An at-the-money option has a delta near ±0.50.

Gamma (Γ) measures how fast delta itself changes when the stock moves. High gamma means delta shifts rapidly, requiring more frequent rebalancing. Short option positions have negative position gamma — the hedged P/L decreases when the stock makes large moves in either direction. This is the primary risk in a delta-hedged short option position.

How to Read the P/L Chart

The solid blue line (At Expiration) shows the hedged P/L across stock prices at option expiration. The chart has a kink at the strike price (K), not the current stock price, because that is where the option payoff changes from intrinsic to zero. For short options the shape is an inverted V (gamma loss from large moves); for long options it is a V shape (gamma profit from large moves).

The dashed dark blue line (Today / T+0) represents the theoretical hedged P/L today, computed by repricing the option with Black-Scholes at each stock price. The curve is approximately parabolic near the entry price (reflecting second-order gamma behavior), becoming asymmetric over wider price ranges. Short options produce a downward curve (negative position gamma); long options produce an upward curve (positive position gamma). The T+0 curve passes through zero at the current stock price (where both option and hedge P/L are zero by construction). The expiration curve passes through zero at the current price only when the option is at-the-money; for non-ATM options, the expiration P/L at the entry price equals the option premium value since the hedge P/L is zero there.

IV Mode vs. Manual Mode

IV Mode: Enter implied volatility, and the calculator uses Black-Scholes to compute the option premium, delta, and gamma. This mode also enables the “Today (T+0)” P/L curve on the chart.

Manual Mode: Enter the exact premium and delta from your broker’s platform. Useful when you know the precise values. Only the expiration payoff curve is shown because IV is needed to compute theoretical values before expiration. Gamma shows “N/A” in this mode.

When to Use Delta Hedging

• You have sold options (e.g., short calls or puts) and want to remove directional risk while keeping exposure to time decay
• You are a market maker or systematic trader who needs to stay delta-neutral
• You want to isolate volatility exposure (vega) from directional exposure (delta)
• You want to understand how gamma risk affects a hedged position
• You are studying options Greeks and want to see how delta and gamma translate into real P/L