# Delta Hedging

> Delta hedging offsets an option position's directional risk with the underlying. Learn how it works, how often to rehedge and what risk remains.

Source: https://learn.tradelabsai.com/options/delta-hedging/  
Track: Options · Level: Advanced · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Delta Hedging", https://learn.tradelabsai.com/options/delta-hedging/

Delta hedging means taking a position in the underlying asset that offsets the delta of an option position, so that small moves in the underlying have little effect on total profit or loss. A trader who is long calls with a combined delta of 300 shares can short 300 shares to become delta neutral. Market makers delta hedge almost everything they trade, and volatility traders use it to isolate the part of an option's value that depends on volatility rather than direction.

## The basic mechanics

```
shares to hedge = minus (option delta × 100 × number of contracts)
```

**Example: Hedging a long call position**
You buy 20 calls on a $50 stock, each with delta 0.45. Position delta: 20 × 0.45 × 100 = 900. To be delta neutral, you short 900 shares.

- **Stock rises $1:** calls gain about $0.45 × 2,000 = $900; short stock loses $900. Net change: about zero, plus a little gain from gamma.
- **Stock falls $1:** calls lose about $900; short stock gains $900. Again, about zero.

You now hold a position whose value depends mostly on volatility and time, not direction.

## Why the hedge does not stay neutral

Delta changes constantly:

- **Price moves change delta** through [Gamma](https://learn.tradelabsai.com/options/gamma/).
- **Time passing changes delta** through charm.
- **Volatility changes change delta** through vanna. See [Charm, Vanna and Volga](https://learn.tradelabsai.com/options/charm-vanna-and-volga/).

A hedge set in the morning may be far from neutral by the afternoon. Traders rehedge periodically, buying or selling the underlying to bring delta back to zero.

## Long gamma hedging vs short gamma hedging

| | Long options (long gamma) | Short options (short gamma) |
|---|---|---|
| Price rises | Delta rises; sell shares to rehedge | Delta falls; buy shares to rehedge |
| Price falls | Delta falls; buy shares to rehedge | Delta rises; sell shares to rehedge |
| Pattern | Sell high, buy low | Buy high, sell low |
| Time decay | Pay theta | Collect theta |

Long gamma hedgers naturally trade against the market and lock in small gains on each rehedge; this is [Gamma Scalping](https://learn.tradelabsai.com/options/gamma-scalping/). Short gamma hedgers must chase the market, buying after rises and selling after falls, which costs them money. They are compensated by the theta they collect.

## How often to rehedge

| Approach | Description | Trade off |
|---|---|---|
| Time based | Rehedge at fixed intervals, such as hourly or daily | Simple; may miss big intraday moves |
| Threshold based | Rehedge when delta exceeds a band, such as 100 shares | Responds to moves; trades more in volatile markets |
| Continuous (theory) | Rehedge constantly | Impossible in practice because of costs |

More frequent rehedging tracks the theory better but costs more in spreads and commissions. See [Transaction Costs](https://learn.tradelabsai.com/orders/transaction-costs/).

## What determines profit on a hedged option

The Black Scholes model assumes continuous hedging. Under its assumptions, a delta hedged option earns or loses based on the difference between actual (realised) volatility and the implied volatility paid:

- **Bought options at 20% implied volatility, market moves at 30% realised:** hedging gains exceed theta paid; profit.
- **Bought at 20%, market moves at 12% realised:** theta exceeds hedging gains; loss.

This is the foundation of volatility trading. See [Implied Volatility (IV)](https://learn.tradelabsai.com/volatility/implied-volatility/), [Historical and Realized Volatility](https://learn.tradelabsai.com/volatility/historical-volatility/) and [Volatility Trading](https://learn.tradelabsai.com/volatility/volatility-trading/).

## Who delta hedges

- **Market makers** hedge almost every trade to stay neutral and earn the spread. See [Market Making](https://learn.tradelabsai.com/strategies/market-making/).
- **Banks** hedge options sold to clients, including structured products.
- **Volatility traders** hedge to isolate volatility exposure.
- **Funds** hedge equity exposure in convertible bond arbitrage and similar strategies.

Aggregate dealer hedging can affect markets. When dealers are short gamma, their hedging adds to moves; when long gamma, it dampens them. See [Dealer Gamma Exposure](https://learn.tradelabsai.com/options/dealer-gamma-exposure/).

## Limits of delta hedging

- **Gap risk:** prices can jump overnight, past any hedge.
- **Costs:** frequent rehedging adds up.
- **Model error:** delta depends on the volatility assumption, so the hedge ratio can be wrong.
- **Liquidity:** hedging large positions can move the market. See [Market Impact](https://learn.tradelabsai.com/orders/market-impact/).

## Common mistakes

- **Hedging once and forgetting.**
- **Ignoring rehedging costs** in strategy planning.
- **Thinking a delta neutral position has no risk.** Gamma, vega and gap risk remain.

## Frequently asked questions

### What is delta hedging?

Offsetting the delta of an option position with an opposite position in the underlying, so small price moves have little net effect.

### How often should you rehedge?

It depends on gamma, volatility and costs. Traders rehedge at fixed times or when delta moves outside a set band.

### Does delta hedging remove all risk?

No. It removes small directional risk, but gamma, vega, gap moves and costs still affect profit or loss.

Next, see how long gamma traders profit from rehedging in [Gamma Scalping](https://learn.tradelabsai.com/options/gamma-scalping/).

## Continue learning

- Next lesson: [Gamma Scalping](https://learn.tradelabsai.com/options/gamma-scalping/)
- Previous lesson: [Charm, Vanna and Volga](https://learn.tradelabsai.com/options/charm-vanna-and-volga/)
- Related: [Charm, Vanna and Volga](https://learn.tradelabsai.com/options/charm-vanna-and-volga/): Charm, vanna and volga measure how delta and vega change with time, volatility and price. Learn what each means and why dealers and volatility traders watch them.
- Related: [Delta](https://learn.tradelabsai.com/options/delta/): Delta measures how much an option's price moves for a $1 move in the underlying. Learn delta for calls and puts, delta as a hedge ratio and as a rough probability.
- Related: [Gamma Scalping](https://learn.tradelabsai.com/options/gamma-scalping/): Gamma scalping buys options and repeatedly delta hedges to lock in gains from price swings. Learn how it works, the break even move and when it pays.
- Related: [Market Making](https://learn.tradelabsai.com/strategies/market-making/): Market making quotes both a buy and a sell price to earn the bid ask spread. Learn how market makers manage inventory, adverse selection and risk.
- Related: [Managing Portfolio Greeks](https://learn.tradelabsai.com/options/managing-portfolio-greeks/): Learn to add up delta, gamma, theta and vega across many option positions, set limits, run scenarios and adjust a book so its risks match your intentions.
- Related: [Dealer Gamma Exposure](https://learn.tradelabsai.com/options/dealer-gamma-exposure/): Dealer gamma exposure estimates how option dealers' hedging may dampen or amplify moves. Learn how GEX is calculated, what it suggests and its big limitations.