Calculator Inputs
Use the responsive grid below. Large screens show three columns, smaller screens show two, and mobile shows one.
Plotly Graph
The graph shows how target hedge shares change as option delta moves from -1 to 1.
Formula Used
1) Option Delta Exposure
Option Delta Exposure = Position Sign × Contracts × Contract Multiplier × Delta
2) Target Hedge Shares
Target Hedge Shares = - Option Delta Exposure × Hedge Ratio
3) Shares to Buy or Sell Today
Shares to Trade = Target Hedge Shares - Current Hedge Shares Held
4) Net Delta After Rebalancing
Ending Net Delta = Option Delta Exposure + Current Shares + Shares to Trade
How to Use This Calculator
Calculate the Number of Shares to Buy or Sell on Day 1 to Maintain the Delta Hedge
Use this rule:
Day 1 Shares to Trade = Target Hedge Shares - Current Hedge Shares Held.
A positive result means buy shares. A negative result means sell shares.
Example: short 10 call contracts with delta 0.55 and multiplier 100 creates an option delta exposure of -550. To hedge fully, target stock shares are +550. If you already hold 450 shares, then day 1 trade equals 550 - 450 = buy 100 shares.
Example Data Table
| Day | Position | Contracts | Delta | Multiplier | Target Hedge Shares | Current Shares | Trade Required |
|---|---|---|---|---|---|---|---|
| Day 0 | Short Call | 10 | 0.50 | 100 | 500 | 500 | 0 |
| Day 1 | Short Call | 10 | 0.55 | 100 | 550 | 450 | Buy 100 |
| Day 2 | Short Call | 10 | 0.48 | 100 | 480 | 550 | Sell 70 |
FAQs
1) What is delta hedging?
Delta hedging offsets option delta exposure with stock shares. The goal is to keep the combined position close to delta neutral after market changes.
2) How are hedge shares calculated?
Multiply contracts, contract multiplier, and option delta, then apply the position sign. Reverse that exposure to get the target hedge shares. Compare target shares with current shares to find today’s trade.
3) Why can delta be negative?
Put options usually have negative delta. A short option position also reverses the sign of the option’s exposure. This calculator keeps the sign so the hedge direction stays correct.
4) How do I calculate the number of shares to buy or sell on day 1?
Subtract current hedge shares from target hedge shares. Positive output means buy that many shares. Negative output means sell the absolute amount to restore the delta hedge.
5) Why does the contract multiplier matter?
The multiplier converts one option contract into equivalent share exposure. Equity options often use 100 shares per contract, so hedge size changes sharply with multiplier size.
6) Does zero net delta remove all risk?
No. Delta neutrality reduces first-order price sensitivity only. Gamma, theta, vega, transaction costs, and gaps can still create gains or losses after the hedge is set.
7) How often should I rebalance a delta hedge?
Rebalancing frequency depends on volatility, liquidity, risk tolerance, and trading costs. Faster-moving positions usually need more frequent adjustment because delta changes as price and time change.
8) Can this calculator handle long and short option positions?
Yes. Choose long or short in the position field. The calculator applies the correct exposure sign and then computes target hedge shares and the required trade.