name

bull-call-spread

description

Analyzes bull-call-spread debit spreads for bullish directional plays with defined risk. Requires numpy>=1.24.0, pandas>=2.0.0, matplotlib>=3.7.0, scipy>=1.10.0. Use when expecting moderate price increase, comparing vertical spread configurations, analyzing debit spread opportunities, calculating Greeks for multi-leg positions, or evaluating defined-risk bullish strategies on liquid optionable securities.

Bull Call Spread Strategy

Version: 2.0 Last Updated: 2025-12-12

Overview

A bull-call-spread is a vertical debit spread that profits from moderate upward price movement while limiting both risk and reward. The strategy involves buying a lower-strike call (long call) and selling a higher-strike call (short call), creating a net debit position with defined maximum loss and profit.

Quick Summary: Buy lower call + Sell higher call = Defined-risk bullish play

Previous Version: v1.0 had comprehensive inline documentation (823 lines). v2.0 refactored to progressive disclosure (<500 lines) following SKILL_PACKAGE_TEMPLATE v3.0.

Strategy Characteristics

Position Structure:

Buy 1 call at lower strike (long call)
Sell 1 call at higher strike (short call)
Same expiration date
Same underlying stock

Risk Profile:

Maximum Loss: Net debit paid (long premium - short premium)
Maximum Profit: Spread width - Net debit
Breakeven: Long strike + Net debit
Best Use: Moderately bullish outlook with defined risk parameters

Cost Components:

Long call premium (debit)
Short call premium (credit)
Net debit = Long premium - Short premium
Transaction costs: ~$0.65 per contract × 2 legs = $1.30

Quick Start

Calculate bull-call-spread metrics:

from scripts.strategy_calculator import BullCallSpread

# Example: Bullish on SPY at $450
position = BullCallSpread(
    underlying_symbol="SPY",
    underlying_price=450.00,
    long_strike=445.00,    # Buy $5 ITM call
    short_strike=455.00,   # Sell $5 OTM call
    long_premium=8.50,
    short_premium=3.20,
    contracts=1
)

# Key metrics
print(f"Max Profit: ${position.max_profit:.2f}")
print(f"Max Loss: ${position.max_loss:.2f}")
print(f"Breakeven: ${position.breakeven_price:.2f}")
print(f"Risk/Reward: {position.risk_reward_ratio:.2f}")

Core Workflow

1. Market Analysis

Identify bullish opportunity with moderate upside target.

Criteria:

Technical breakout (resistance break, bullish pattern)
Positive fundamental catalyst
Uptrend confirmation
Target price identified

2. Strike Selection

Long Call (Lower Strike):

Typically ATM or slightly ITM
Delta: 0.50-0.65
Provides directional exposure

Short Call (Higher Strike):

OTM above long strike
Delta: 0.25-0.40
Reduces cost, defines max profit

Common Spread Widths:

Narrow ($2.50-$5): Lower cost, lower profit
Standard ($5-$10): Balanced risk/reward
Wide ($10-$20): Higher cost, higher profit potential

See reference.md for delta-based framework.

3. Spread Width Analysis

Compare spread configurations:

from scripts.strategy_calculator import analyze_spread_widths

# Compare $2.50, $5, $10 spreads
results = analyze_spread_widths(
    underlying_price=450.00,
    long_strike=445.00,
    spread_widths=[2.5, 5.0, 10.0],
    volatility=0.20,
    days_to_expiration=45
)

# Analyze return on risk for each width
for width, metrics in results.items():
    print(f"${width} spread: ROR {metrics['return_on_risk']:.1f}%")

See reference.md for optimization framework.

4. Expiration Cycle Selection

Standard Cycles:

30-45 days: Optimal theta decay, standard choice
45-60 days: More time for thesis to play out
60-90 days: Reduced urgency, lower theta

Considerations:

Time for bullish thesis to materialize
Theta decay acceleration (30-45 DTE sweet spot)
Upcoming events (earnings, Fed meetings)

5. Position Sizing

Calculate appropriate contracts based on portfolio risk:

from scripts.strategy_calculator import calculate_position_size

contracts = calculate_position_size(
    portfolio_value=100000,
    risk_per_trade=0.02,      # 2% portfolio heat
    max_loss_per_contract=530  # Net debit
)
# Returns: 3 contracts (max risk $1,590 = 1.59%)

See reference.md.

6. Greeks Analysis

Monitor position Greeks:

from scripts.strategy_calculator import calculate_spread_greeks

greeks = calculate_spread_greeks(
    long_strike=445.00,
    short_strike=455.00,
    underlying_price=450.00,
    volatility=0.20,
    time_to_expiration=45/365
)

print(f"Delta: {greeks['delta']:.3f}")    # Positive (bullish)
print(f"Theta: {greeks['theta']:.3f}")    # Negative (time decay hurts)
print(f"Vega: {greeks['vega']:.3f}")      # Positive initially (IV sensitivity)

See reference.md for comprehensive Greeks guide.

7. Entry Execution

Order Types:

Limit Order: Specify max net debit willing to pay
Market Order: Immediate fill (wider slippage)
Vertical Spread Order: Single order for both legs

Best Practices:

Enter as single spread order (better pricing)
Set limit at mid-point of bid/ask spread
Adjust limit if not filled within 30 seconds
Avoid wide markets (>10% spread width)

8. Management and Exit

Profit Targets:

50% max profit: Close early, reduce risk
75% max profit: Near maximum, theta slowing
Max profit: Hold to expiration (if confident)

Stop Loss:

100% of debit: Full loss, thesis invalidated
150% of debit: Avoid if spread widens against you

Adjustments:

Roll up: Higher both strikes if more bullish
Roll out: Extend expiration if need more time
Close early: Take profits or cut losses

See reference.md for detailed adjustment strategies.

Scripts

Calculator

# Calculate bull-call-spread metrics
python scripts/strategy_calculator.py \
  --underlying SPY \
  --price 450 \
  --long-strike 445 \
  --short-strike 455 \
  --long-premium 8.50 \
  --short-premium 3.20 \
  --contracts 1

Black-Scholes Pricing

# Price individual options
python scripts/black_scholes.py \
  --type call \
  --spot 450 \
  --strike 445 \
  --time 0.123 \
  --rate 0.05 \
  --volatility 0.20

Spread Analyzer

# Compare multiple spread widths
python scripts/strategy_calculator.py \
  --analyze-widths \
  --underlying SPY \
  --price 450 \
  --long-strike 445 \
  --widths 2.5 5.0 10.0 \
  --dte 45

References

Core Documentation

reference.md - Complete mathematical derivations and advanced topics
- Strike Selection Guidelines
- Spread Width Optimization
- Greeks Analysis Detailed
- Position Sizing Framework
- Management and Adjustments
- Scenario Analysis
- Historical Performance

Code Examples

scripts/strategy_calculator.py - Main calculator with CLI
scripts/black_scholes.py - Options pricing engine

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 spread width - net debit
Directional Risk: Requires upward movement to profit
Time Decay: Theta works against long call if stock doesn't move
Assignment Risk: Short call may be assigned if ITM at expiration
Early Assignment: Possible if short call goes deep ITM (rare on index options)

Risk Mitigation:

Define max loss before entry (net debit paid)
Use stop loss at 100-150% of debit
Avoid holding through earnings (IV crush risk)
Monitor short call for early assignment (if deep ITM)
Size positions appropriately (2-5% portfolio heat)

When to Use Bull Call Spread

✅ Ideal Scenarios:

Moderately bullish outlook (5-15% upside expected)
Want defined risk and defined reward
Prefer lower cost than buying calls outright
Time horizon: 30-60 days
Normal to elevated IV environment

❌ Avoid When:

Strongly bullish (>20% move expected) - consider long calls
Neutral outlook - use different strategy
Very low IV - debit may be too high for good R:R
Need unlimited profit potential - use long calls

Comparison to Other Strategies

vs. Long Call:

✅ Lower cost (short call reduces debit)
❌ Limited profit (capped at spread width)
✅ Defined risk with better R:R ratio

vs. Call Ratio Spread:

✅ Simpler structure (1:1 ratio)
✅ No naked short exposure
❌ Lower profit potential

vs. Bear Put Spread:

✅ Opposite direction (bullish vs bearish)
✅ Similar risk/reward profile
✅ Same debit spread structure

Example Trade

Scenario: SPY at $450, expecting rally to $455-460 over 45 days

Setup:

Buy 1 SPY $445 call @ $8.50 (debit)
Sell 1 SPY $455 call @ $3.20 (credit)
Net debit: $5.30 × 100 = $530 per spread
Contracts: 3 (based on 2% portfolio risk on $80k account)