Long Call Butterfly

Long Call Butterfly Strategy

Version: 1.0 Last Updated: 2025-12-12

Overview

A long call butterfly is a sophisticated neutral strategy that profits from minimal price movement. Using three strike prices with four option contracts (1 ITM call + 2 ATM calls + 1 OTM call), the strategy offers limited risk and limited reward with maximum profit achieved when the stock closes exactly at the middle strike at expiration.

Quick Summary: Buy lower call + Sell 2 middle calls + Buy upper call = Profit from no movement

Strategy Characteristics

Position Structure:

• Buy 1 call at lower strike (ITM or ATM)
• Sell 2 calls at middle strike (ATM)
• Buy 1 call at upper strike (OTM)
• All same expiration, equal spacing between strikes

Risk Profile:

• Maximum Loss: Net debit paid (limited)
• Maximum Profit: Middle strike - Lower strike - Net debit
• Breakeven Points:
  • Lower: Lower strike + Net debit
  • Upper: Upper strike - Net debit
• Best Use: Expect stock to pin near middle strike with low volatility

Cost Components:

• Lower call premium: Paid (debit, expensive)
• Middle calls premium: Received (credit × 2, offset cost)
• Upper call premium: Paid (debit, cheap)
• Net debit = Lower + Upper - (2 × Middle)
• Transaction costs: ~$0.65 per contract × 4 legs = $2.60

Quick Start

Calculate butterfly metrics:

from scripts.butterfly_calculator import LongCallButterfly

# Example: SPY at $450, expect minimal movement
position = LongCallButterfly(
    underlying_price=450.00,
    lower_strike=445.00,    # $5 ITM
    middle_strike=450.00,   # ATM (body)
    upper_strike=455.00,    # $5 OTM
    lower_premium=8.50,
    middle_premium=5.00,    # Sold 2×
    upper_premium=2.50,
    contracts=1
)

# Key metrics
print(f"Net Debit: ${position.net_debit:.2f}")
print(f"Max Profit: ${position.max_profit:.2f}")
print(f"Max Loss: ${position.max_loss:.2f}")
print(f"Breakevens: ${position.lower_breakeven:.2f} - ${position.upper_breakeven:.2f}")
print(f"Profit Zone: {position.profit_zone_width:.2f} points")

Core Workflow

1. Identify Low-Volatility Opportunity

Look for stocks likely to trade in tight range:

Ideal Scenarios:

• Post-Earnings Calm: Stock settles after volatile earnings
• Consolidation: Trading in well-defined range
• Technical Levels: Near strong support/resistance
• Pre-Event Lull: Quiet period before catalyst
• Low IV Environment: IV rank <40, low expected move

Stock Characteristics:

• Low beta (< 1.0)
• Tight historical trading ranges
• Low implied volatility
• Recent volatility compression
• Clear technical pivot level

See references/opportunity-identification.md.

2. Strike Selection Framework

Standard Butterfly (Equal Wing Spacing):

• Lower: $5 below current price
• Middle: At current price (ATM)
• Upper: $5 above current price
• Wing width: $5 both sides
• Example: Stock $100 → $95/$100/$105

Narrow Butterfly ($2.50-$5 wings):

• Tighter profit zone
• Higher probability of profit
• Lower max profit potential
• Example: Stock $450 → $447.50/$450/$452.50

Wide Butterfly ($10-$20 wings):

• Wider profit zone
• Lower probability of max profit
• Higher max profit potential
• Example: Stock $100 → $90/$100/$110

Selection Rules:

• Middle strike = Expected pin point (often ATM)
• Equal spacing: Upper-Middle = Middle-Lower
• Match wing width to expected range

See references/strike-selection-guide.md.

3. Wing Width Optimization

Compare different wing widths:

from scripts.wing_optimizer import analyze_wing_widths

results = analyze_wing_widths(
    underlying_price=450.00,
    wing_widths=[2.5, 5.0, 10.0],
    volatility=0.18,
    days_to_expiration=30
)

for width, metrics in results.items():
    print(f"${width} wings:")
    print(f"  Max Profit: ${metrics['max_profit']:.2f}")
    print(f"  Max Loss: ${metrics['max_loss']:.2f}")
    print(f"  Profit Zone: ${metrics['profit_zone_width']:.2f}")
    print(f"  Prob of Profit: {metrics['prob_profit']:.1f}%")

Trade-off:

• Narrow wings: Higher prob, lower profit
• Wide wings: Lower prob, higher profit

See references/wing-width-analysis.md.

4. Probability Analysis

Calculate probability of profit:

from scripts.probability_calculator import calculate_butterfly_probabilities

prob = calculate_butterfly_probabilities(
    underlying_price=450.00,
    lower_strike=445.00,
    middle_strike=450.00,
    upper_strike=455.00,
    volatility=0.18,
    days_to_expiration=30
)

print(f"Prob at Middle Strike: {prob['at_middle']:.1f}%")
print(f"Prob in Profit Zone: {prob['in_profit_zone']:.1f}%")
print(f"Prob of Max Profit: {prob['max_profit']:.1f}%")
print(f"Prob of Max Loss: {prob['max_loss']:.1f}%")
print(f"Expected Value: ${prob['expected_value']:.2f}")

Decision Criteria:

• Prob in profit zone >60%: Good setup
• Expected value >0: Positive expectancy
• Max profit/Max loss ratio >3:1: Favorable R:R

See references/probability-analysis.md.

5. Expiration Cycle Selection

Short-Term Butterflies (7-21 days):

• Lower cost (less time premium)
• Faster theta decay benefit
• Less time for stock to move outside range
• Higher gamma risk (rapid changes)
• Best for: Near-term pinning opportunities

Medium-Term Butterflies (30-45 days):

• Balanced cost and time
• Standard approach
• Moderate theta benefit
• Reasonable gamma exposure
• Best for: Standard neutral plays

Long-Term Butterflies (60-90 days):

• Higher cost (more time premium)
• Slow theta decay
• More time for adjustment
• Lower gamma risk
• Best for: Patient, adjustment-friendly approach

See references/expiration-timing.md.

6. Greeks Analysis

Monitor butterfly Greeks:

from scripts.greeks_calculator import calculate_butterfly_greeks

greeks = calculate_butterfly_greeks(
    lower_strike=445.00,
    middle_strike=450.00,
    upper_strike=455.00,
    underlying_price=450.00,
    volatility=0.18,
    time_to_expiration=30/365
)

print(f"Delta: {greeks['delta']:.3f}")    # ~0 at middle
print(f"Gamma: {greeks['gamma']:.3f}")    # Changes rapidly
print(f"Theta: {greeks['theta']:.3f}")    # Positive (earns decay)
print(f"Vega: {greeks['vega']:.3f}")      # Negative (hurts from IV rise)

Key Insights:

• Delta: Near zero at middle strike, changes outside wings
• Gamma: Positive in profit zone, negative outside
• Theta: Positive (benefits from time decay)
• Vega: Negative (benefits from IV decrease)

See references/greeks-guide.md.

7. Position Sizing

Calculate appropriate contracts:

from scripts/position_sizer import calculate_butterfly_size

contracts = calculate_butterfly_size(
    portfolio_value=100000,
    risk_per_trade=0.01,      # 1% max risk
    max_loss_per_butterfly=150 # Net debit
)
# Returns: 6 contracts (max risk $900 = 0.9%)

Sizing Guidelines:

• Risk 0.5-2% per butterfly (low risk strategy)
• Max loss = Net debit (clearly defined)
• Consider multiple butterflies at different strikes
• Scale in/out rather than all-in

See references/position-sizing.md.

8. Entry Execution

Order Types:

• Butterfly Order: Single order for all 4 legs (best execution)
• Limit Order: Set max net debit willing to pay
• Spread Order: Enter as vertical spreads (2 separate orders)

Best Practices:

• Always enter as butterfly order (1 ticket, 4 legs)
• Set limit at mid-point of butterfly bid/ask
• Adjust by $0.05 if not filled within 60 seconds
• Avoid wide markets (>15% spread)
• Verify equal wing spacing before sending

Entry Timing:

• Enter when stock at middle strike (optimal)
• Avoid entering after large move
• Best during low volatility periods
• Consider multiple strikes if uncertain of pin point

9. Adjustment Strategies

Stock Moves Outside Profit Zone:

Upside Adjustment (Stock above upper strike):

• Close entire butterfly, accept loss
• Roll to higher strikes (all 3 strikes up)
• Add short call spread above (convert to condor)

Downside Adjustment (Stock below lower strike):

• Close entire butterfly, accept loss
• Roll to lower strikes (all 3 strikes down)
• Add short put spread below (convert to condor)

Widening Profit Zone:

• Close current butterfly
• Open wider wing butterfly (increase spacing)
• Accept lower max profit for wider range

See references/adjustment-techniques.md.

10. Exit Management

Profit Targets:

• 50-70% max profit: Excellent target, reduces risk
• 80% max profit: Near optimal, theta slowing
• Expiration: Hold for max profit if confident

Stop Loss:

• 100% of debit: Full max loss, exit immediately
• Stock outside wings: Low recovery probability
• Volatility spike: Exit if IV increases significantly

Early Exit Scenarios:

• Stock moves >75% toward wing
• IV increases >50% (vega loss)
• Theta benefit exhausted (little time value left)
• Better opportunity elsewhere

See references/exit-strategies.md.

Scripts

Calculator

# Calculate butterfly metrics
python scripts/butterfly_calculator.py \
  --underlying SPY \
  --price 450 \
  --lower-strike 445 \
  --middle-strike 450 \
  --upper-strike 455 \
  --lower-premium 8.50 \
  --middle-premium 5.00 \
  --upper-premium 2.50

Wing Optimizer

# Compare different wing widths
python scripts/wing_optimizer.py \
  --underlying SPY \
  --price 450 \
  --widths 2.5 5.0 10.0 \
  --dte 30 \
  --volatility 0.18

Probability Calculator

# Calculate probability of profit
python scripts/probability_calculator.py \
  --price 450 \
  --lower 445 \
  --middle 450 \
  --upper 455 \
  --dte 30 \
  --vol 0.18

References

Core Guides

• quickstart-guide.md - 5-minute overview
• installation-guide.md - Setup instructions
• developer-guide.md - Code standards

Strategy-Specific

• opportunity-identification.md - Finding low-vol setups
• strike-selection-guide.md - Equal wing spacing framework
• wing-width-analysis.md - Optimize wing spacing
• probability-analysis.md - Calculate profit probabilities
• expiration-timing.md - 7/30/60 day comparison
• greeks-guide.md - Delta, gamma, theta, vega
• position-sizing.md - Risk management
• adjustment-techniques.md - Managing outside wings
• exit-strategies.md - Profit targets, stop loss
• examples.md - Real consolidation plays

Dependencies

Required Packages:

numpy>=1.24.0
pandas>=2.0.0
matplotlib>=3.7.0
scipy>=1.10.0

Installation:

pip install -r requirements.txt

Python Version: 3.11+

Risk Warnings

⚠️ Key Risks:

• Limited Profit: Capped at wing width - net debit
• Narrow Profit Zone: Small range for profitability
• Gamma Risk: Rapid position changes outside wings
• Assignment Risk: Short middle calls can be assigned early
• Pin Risk: Stock settling exactly at strike (complex assignment scenarios)
• Complexity: 4 legs = higher commissions, wider spreads
• Adjustment Cost: Expensive to roll or adjust position

Risk Mitigation:

• Only use in low volatility environments
• Set stop loss at max loss (net debit)
• Exit early if stock approaches wings (don't wait)
• Monitor middle strike for early assignment risk
• Use stocks with liquid options (tight spreads)
• Verify equal wing spacing to avoid undefined risk

When to Use Long Call Butterfly

✅ Ideal Scenarios:

• Expect minimal price movement (neutral outlook)
• Stock consolidating in tight range
• Post-earnings quiet period
• Low IV environment (IV rank <40)
• Near strong technical support/resistance
• Want defined risk with low capital requirement
• Comfortable with limited profit potential

❌ Avoid When:

• Expecting large moves (use straddle/strangle)
• High volatility environment (IV crush hurts)
• Unclear where stock will settle
• Wide bid/ask spreads (execution cost too high)
• Trending market (directional bias)
• Upcoming catalyst (volatility spike risk)

Comparison to Other Strategies

vs. Iron Butterfly:

• ✅ All long options (no naked short risk)
• ❌ Pay debit vs. collect credit
• ✅ Easier approval (no margin requirement)

vs. Straddle/Strangle:

• ✅ Lower cost (credit from short middle calls)
• ❌ Limited profit (capped vs. unlimited)
• ✅ Profits from no movement (vs. needing big move)

vs. Condor:

• ❌ Narrower profit zone
• ✅ Higher max profit potential
• ✅ Lower cost (fewer legs)

Example Trade

Scenario: SPY consolidating at $450, expect to stay $445-$455 over 30 days

Setup:

• Buy 1 SPY $445 call @ $8.50
• Sell 2 SPY $450 calls @ $5.00 (receive $10.00)
• Buy 1 SPY $455 call @ $2.50
• Net debit: $8.50 + $2.50 - $10.00 = $1.00 × 100 = $100
• Contracts: 10 butterflies
• Expiration: 30 days

Risk Profile:

• Max Loss: $100 × 10 = $1,000 (if SPY ≤$445 or ≥$455)
• Max Profit: ($5.00 - $1.00) × 100 × 10 = $4,000 (if SPY exactly $450)
• Lower Breakeven: $445 + $1 = $446
• Upper Breakeven: $455 - $1 = $454
• Profit Zone: $446-$454 (8-point range, ±1.8%)
• Risk/Reward: 1:4 (excellent)

Outcomes at Expiration:

• SPY at $450: Max profit $4,000
• SPY at $452: Profit ~$2,000 (in profit zone)
• SPY at $446: Near breakeven
• SPY at $443: Max loss $1,000
• SPY at $457: Max loss $1,000

Version History

v1.0 (2025-12-12)

• Initial release using SKILL_PACKAGE_TEMPLATE v3.0
• Anthropic + Claude Code compliant (<500 lines)
• Progressive disclosure with references/
• Complete wing width optimizer and probability calculator
• Adjustment techniques and exit strategies
• Equal spacing framework for strike selection

Compliance: Anthropic Best Practices ✅ | Claude Code Compatible ✅ Template: SKILL_PACKAGE_TEMPLATE v3.0 Lines: ~480 (under 500-line limit)