Delta-Gamma Analysis Calculator

Delta and Gamma are primary "Greeks" that measure an option's price sensitivity to changes in the underlying asset's price. This calculator helps you analyze how your options positions respond to price changes and provides the data needed for effective hedging.

When to use this calculator:

  • When you need to understand your directional exposure from options positions
  • When creating delta-neutral strategies or hedging existing positions
  • When assessing potential profits or losses from price movements
  • When evaluating how fast delta changes as the underlying price moves
  • When determining the appropriate number of shares needed to hedge an options position

Delta-Gamma Analysis

Analyze price sensitivity and hedging requirements

Understanding Delta and Gamma

Delta (Δ)

Delta measures the rate of change in an option's price relative to changes in the underlying asset's price.

  • • Call Option Delta: Ranges from 0 to 1
  • • Put Option Delta: Ranges from -1 to 0
  • • At-the-money options: Delta is approximately 0.50 (calls) or -0.50 (puts)
  • • Delta also represents: The approximate probability that the option will expire in-the-money

Example: A call option with a delta of 0.60 will theoretically increase in value by $0.60 if the underlying stock rises by $1.00.

Gamma (Γ)

Gamma measures the rate of change in an option's delta relative to changes in the underlying asset's price.

  • • Higher Gamma: Delta changes more rapidly with price movements
  • • Highest at: At-the-money options with less time to expiration
  • • Always positive: For both calls and puts
  • • Convexity measure: Describes the "acceleration" of option price changes

Example: An option with a gamma of 0.08 means its delta will change by 0.08 for each $1 move in the underlying stock.

Calculator Fields Explained

  • Stock Price:

    The current market price of the underlying asset.

  • Strike Price:

    The price at which the option can be exercised.

  • Days to Expiry:

    Number of calendar days until the option expires.

  • Volatility:

    The expected annual volatility of the underlying asset (in %).

  • Interest Rate:

    Risk-free interest rate used in the Black-Scholes model.

  • Option Type:

    Call (right to buy) or Put (right to sell).

Results Explained

Basic Metrics

  • Delta:

    The rate of change of option price with respect to changes in the underlying price. Represents the directional exposure.

  • Gamma:

    The rate of change of delta with respect to changes in the underlying price. Measures delta's sensitivity to price moves.

Practical Applications

  • Delta Notional:

    The dollar value of exposure to price movements. Calculated as Delta × Stock Price × Contract Multiplier (100).

  • Gamma Notional:

    The dollar change in delta exposure for a 1% move in the stock. Shows how quickly your exposure changes.

  • Hedge Shares:

    The number of shares needed to create a delta-neutral position. Calculated as -Delta × Contract Multiplier (100).

Practical Applications

  • Directional Exposure Management: Use delta to understand your portfolio's exposure to market movements
  • Delta Hedging: Create market-neutral strategies by balancing positive and negative deltas
  • Risk Management: Quantify potential P&L impacts from market moves
  • Gamma Scalping: Trading strategy that capitalizes on gamma by rebalancing delta hedges
  • Position Sizing: Use delta to normalize position sizes across different options
  • Options Structure: Design option spreads with specific delta/gamma profiles

Delta Behavior

Understanding how delta behaves:

  • Deep ITM: Delta approaches 1 (calls) or -1 (puts), behaving almost like stock
  • ATM: Delta around 0.5 (calls) or -0.5 (puts), maximum gamma
  • Deep OTM: Delta approaches 0, minimal price reaction to underlying
  • Time effect: As expiration approaches, ITM deltas move closer to 1/-1 and OTM deltas closer to 0

Gamma Behavior

Understanding how gamma behaves:

  • Highest at: ATM options with less time to expiration
  • Long options: Positive gamma (beneficial in volatile markets)
  • Short options: Negative gamma (challenging in volatile markets)
  • Time effect: Gamma increases as expiration approaches for ATM options

Delta-Gamma Hedging Strategies

Delta Hedging

Offsetting delta exposure by taking opposing positions in the underlying asset.

Example: If you're long 3 call options with delta 0.40, you would short 120 shares to neutralize delta.

Gamma Hedging

Adding options positions with offsetting gamma to manage delta changes.

Example: If you have negative gamma from short options, add long options to reduce gamma risk.

Dynamic Hedging

Continuously adjusting your hedge as market prices and greeks change.

Example: Rebalancing your delta hedge when delta changes significantly due to price movements.

Common Pitfalls in Delta-Gamma Trading

  • Over-reliance on Black-Scholes model without considering its limitations
  • Ignoring transaction costs when implementing frequent delta-hedge adjustments
  • Failure to account for other greeks like vega and theta in your analysis
  • Neglecting to adjust volatility inputs as market conditions change
  • Not considering the impact of large overnight gaps when hedging gamma exposure