Options Analytics Methodology

Understanding the mathematical models and market mechanics behind our options analysis

Gamma Squeeze Analysis

Overview

Gamma squeeze analysis identifies stocks with high potential for rapid upward price acceleration due to options dealer hedging dynamics. When dealers sell call options, they must continuously adjust their hedge positions as the stock price moves, creating feedback loops that can accelerate price movements.

Mathematical Foundation

1. Black-Scholes Greeks Calculation

Gamma (Γ): ∂²V/∂S² = N'(d₁) / (S × σ × √T)

Where:
• N'(d₁) = Standard normal probability density function
• S = Current stock price
• σ = Implied volatility
• T = Time to expiration (years)
• d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T)
• K = Strike price
• r = Risk-free rate

Delta (Δ):
• Call: Δ = N(d₁)
• Put: Δ = N(d₁) - 1

N(d₁) = Cumulative standard normal distribution

2. Implied Volatility Estimation

We reverse-engineer IV from market prices using iterative methods:

Given: Market option price
Find: σ such that BS(S, K, T, r, σ) = Market Price

Method: Newton-Raphson or Brent's method
Bounds: σ ∈ [0.01, 3.00] (1% to 300% annualized)

Gamma Exposure Calculation

Core Formula

Near-Money Gamma Exposure = Σ(Gamma × Volume × 100)

For each option contract within 10% of current price:
• Calculate theoretical gamma using Black-Scholes
• Multiply by trading volume
• Multiply by 100 (shares per contract)
• Sum only near-money strikes (0.9 ≤ S/K ≤ 1.1)

Hedge Pressure = Near-Money Gamma × Stock Price
10% Move Impact = Hedge Pressure × (Stock Price × 0.1)

Hedge Pressure (Dollar Value)

Dollar value of stock buying needed per $1 price move. Calculated as near-money gamma × stock price. This converts abstract gamma into actionable dollar impact.

10% Move Impact

Estimated total buying pressure if stock moves 10% higher. Shows potential magnitude of gamma squeeze in billions of dollars.

Dealer Hedging Mechanics

Why Dealers Must Hedge

  1. Dealer sells call option → They are SHORT gamma (negative gamma position)
  2. To remain market-neutral, dealer must maintain delta hedge
  3. As stock price rises, call delta increases
  4. Dealer must buy more shares to maintain hedge
  5. This buying pressure pushes price higher
  6. Higher price → Higher delta → More buying needed (feedback loop)

Hedging Example: TSLA at $442 with $450 Trigger

Stock PriceDelta of $450 CallShares Needed (per 1000 contracts)Action Required
$442 (current)0.4040,000Initial hedge position
$450 (trigger)0.5050,000BUY 10,000 shares
$4550.6060,000BUY 10,000 more shares
$4600.7070,000BUY 10,000 more shares

Note: Gamma is highest at-the-money ($450), so small moves around this level create maximum hedging activity

Ranking System

How Symbols Are Ranked

Symbols are ranked by Hedge Pressure (dollar value of near-money gamma), not raw gamma numbers. This prioritizes stocks where gamma squeeze effects would have the largest market impact.

Example: TSLA vs HOOD

• TSLA: 157k gamma × $442 = $69.4M hedge pressure
• HOOD: 200k gamma × $25 = $5.0M hedge pressure

TSLA ranks higher despite lower gamma because of higher dollar impact.

Why Dollar Impact Matters

A $69M buying pressure move is far more significant for market dynamics than a $5M move, regardless of the underlying gamma numbers.

Key Assumptions & Limitations

Assumptions

  • Dealers maintain delta-neutral positions continuously
  • Risk-free rate assumed at 5% annually
  • Options are European-style for Black-Scholes calculations
  • No dividends during option lifetime
  • Markets are liquid and efficient

Limitations

  • Implied volatility is estimated, not from real-time market data
  • Actual dealer positions are unknown (we assume net short)
  • Does not account for put options' negative gamma
  • Ignores other market participants (only focuses on dealers)
  • Static analysis - doesn't predict timing of moves

How to Use These Signals

Strongest Bullish Signals

Primary Indicators:

  • High rank (#1-3 in hedge pressure)
  • Hedge pressure > $50M per $1 move
  • 10% move impact > $20B buying pressure
  • Trigger level within 5% of current price

Secondary Confirmation:

  • Recent increase in call volume
  • Stock trending upward already
  • Trigger level acts as resistance → breakout target
  • Multiple expirations showing high gamma

Coming Soon: Additional Analytics

Volatility Surface Analysis

IV vs realized volatility, term structure, and volatility smile patterns to identify mispricings

Delta Flow Analysis

Track net delta positioning to identify directional bias and potential support/resistance levels

Multi-Signal Scanner

Combine all 7 continuation signals from the original framework for comprehensive analysis