Options Strategy Advisor

Options Strategy Advisor

Overview

This skill provides comprehensive options strategy analysis and education using theoretical pricing models. It helps traders understand, analyze, and simulate options strategies without requiring real-time market data subscriptions.

Core Capabilities:

• Black-Scholes Pricing: Theoretical option prices and Greeks calculation
• Strategy Simulation: P/L analysis for major options strategies
• Earnings Strategies: Pre-earnings volatility plays integrated with Earnings Calendar
• Risk Management: Position sizing, Greeks exposure, max loss/profit analysis
• Educational Focus: Detailed explanations of strategies and risk metrics

Data Sources:

• FMP API: Stock prices, historical volatility, dividends, earnings dates
• User Input: Implied volatility (IV), risk-free rate
• Theoretical Models: Black-Scholes for pricing and Greeks

Prerequisites

Required:

• Python 3.9+ with numpy, scipy, requests

Optional:

• FMP API key (for real-time stock prices and historical volatility)
• Set via FMP_API_KEY environment variable or --api-key argument
• Without API key: Use manual inputs for stock price and volatility

Installation:

pip install numpy scipy requests

Quick Start Examples:

# Basic call option pricing (no API key needed)
python3 scripts/black_scholes.py

# With FMP API key for real-time data
python3 scripts/black_scholes.py --ticker AAPL --api-key $FMP_API_KEY

# Custom option parameters
python3 scripts/black_scholes.py --stock-price 180 --strike 185 --days 30 --volatility 0.25

# Put option analysis
python3 scripts/black_scholes.py --stock-price 180 --strike 175 --days 30 --option-type put

When to Use This Skill

Use this skill when:

• User asks about options strategies ("What's a covered call?", "How does an iron condor work?")
• User wants to simulate strategy P/L ("What's my max profit on a bull call spread?")
• User needs Greeks analysis ("What's my delta exposure?")
• User asks about earnings strategies ("Should I buy a straddle before earnings?")
• User wants to compare strategies ("Covered call vs protective put?")
• User needs position sizing guidance ("How many contracts should I trade?")
• User asks about volatility ("Is IV high right now?")

Example requests:

• "Analyze a covered call on AAPL"
• "What's the P/L on a $100/$105 bull call spread on MSFT?"
• "Should I trade a straddle before NVDA earnings?"
• "Calculate Greeks for my iron condor position"
• "Compare protective put vs covered call for downside protection"

Supported Strategies

Income Strategies

1. Covered Call - Own stock, sell call (generate income, cap upside) 2. Cash-Secured Put - Sell put with cash backing (collect premium, willing to buy stock) 3. Poor Man's Covered Call - LEAPS call + short near-term call (capital efficient)

Protection Strategies

4. Protective Put - Own stock, buy put (insurance, limited downside) 5. Collar - Own stock, sell call + buy put (limited upside/downside)

Directional Strategies

6. Bull Call Spread - Buy lower strike call, sell higher strike call (limited risk/reward bullish) 7. Bull Put Spread - Sell higher strike put, buy lower strike put (credit spread, bullish) 8. Bear Call Spread - Sell lower strike call, buy higher strike call (credit spread, bearish) 9. Bear Put Spread - Buy higher strike put, sell lower strike put (limited risk/reward bearish)

Volatility Strategies

10. Long Straddle - Buy ATM call + ATM put (profit from big move either direction) 11. Long Strangle - Buy OTM call + OTM put (cheaper than straddle, bigger move needed) 12. Short Straddle - Sell ATM call + ATM put (profit from no movement, unlimited risk) 13. Short Strangle - Sell OTM call + OTM put (profit from no movement, wider range)

Range-Bound Strategies

14. Iron Condor - Bull put spread + bear call spread (profit from range-bound movement) 15. Iron Butterfly - Sell ATM straddle, buy OTM strangle (profit from tight range)

Advanced Strategies

16. Calendar Spread - Sell near-term option, buy longer-term option (profit from time decay) 17. Diagonal Spread - Calendar spread with different strikes (directional + time decay) 18. Ratio Spread - Unbalanced spread (more contracts on one leg)

Analysis Workflow

Step 1: Gather Input Data

Required from User:

• Ticker symbol
• Strategy type
• Strike prices
• Expiration date(s)
• Position size (number of contracts)

Optional from User:

• Implied Volatility (IV) - if not provided, use Historical Volatility (HV)
• Risk-free rate - default to current 3-month T-bill rate (~5.3% as of 2025)

Fetched from FMP API:

• Current stock price
• Historical prices (for HV calculation)
• Dividend yield
• Upcoming earnings date (for earnings strategies)

Example User Input:

Ticker: AAPL
Strategy: Bull Call Spread
Long Strike: $180
Short Strike: $185
Expiration: 30 days
Contracts: 10
IV: 25% (or use HV if not provided)

Step 2: Calculate Historical Volatility (if IV not provided)

Objective: Estimate volatility from historical price movements.

Method:

# Fetch 90 days of price data
prices = get_historical_prices("AAPL", days=90)

# Calculate daily returns
returns = np.log(prices / prices.shift(1))

# Annualized volatility
HV = returns.std() * np.sqrt(252)  # 252 trading days

Output:

• Historical Volatility (annualized percentage)
• Note to user: "HV = 24.5%, consider using current market IV for more accuracy"

User Can Override:

• Provide IV from broker platform (ThinkorSwim, TastyTrade, etc.)
• Script accepts --iv 28.0 parameter

Step 3: Price Options Using Black-Scholes

Black-Scholes Model:

For European-style options:

Call Price = S * N(d1) - K * e^(-r*T) * N(d2)
Put Price = K * e^(-r*T) * N(-d2) - S * N(-d1)

Where:
d1 = [ln(S/K) + (r + σ²/2) * T] / (σ * √T)
d2 = d1 - σ * √T

S = Current stock price
K = Strike price
r = Risk-free rate
T = Time to expiration (years)
σ = Volatility (IV or HV)
N() = Cumulative standard normal distribution

Adjustments:

• Subtract present value of dividends from S for calls
• American options: Use approximation or note "European pricing, may undervalue American options"

Python Implementation:

from scipy.stats import norm
import numpy as np

def black_scholes_call(S, K, T, r, sigma, q=0):
    """
    S: Stock price
    K: Strike price
    T: Time to expiration (years)
    r: Risk-free rate
    sigma: Volatility
    q: Dividend yield
    """
    d1 = (np.log(S/K) + (r - q + 0.5*sigma**2)*T) / (sigma*np.sqrt(T))
    d2 = d1 - sigma*np.sqrt(T)

    call_price = S*np.exp(-q*T)*norm.cdf(d1) - K*np.exp(-r*T)*norm.cdf(d2)
    return call_price

def black_scholes_put(S, K, T, r, sigma, q=0):
    d1 = (np.log(S/K) + (r - q + 0.5*sigma**2)*T) / (sigma*np.sqrt(T))
    d2 = d1 - sigma*np.sqrt(T)

    put_price = K*np.exp(-r*T)*norm.cdf(-d2) - S*np.exp(-q*T)*norm.cdf(-d1)
    return put_price

Output for Each Option Leg:

• Theoretical price
• Note: "Market price may differ due to bid-ask spread and American vs European pricing"

Step 4: Calculate Greeks

The Greeks measure option price sensitivity to various factors:

Delta (Δ): Change in option price per $1 change in stock price

def delta_call(S, K, T, r, sigma, q=0):
    d1 = (np.log(S/K) + (r - q + 0.5*sigma**2)*T) / (sigma*np.sqrt(T))
    return np.exp(-q*T) * norm.cdf(d1)

def delta_put(S, K, T, r, sigma, q=0):
    d1 = (np.log(S/K) + (r - q + 0.5*sigma**2)*T) / (sigma*np.sqrt(T))
    return np.exp(-q*T) * (norm.cdf(d1) - 1)

Gamma (Γ): Change in delta per $1 change in stock price

def gamma(S, K, T, r, sigma, q=0):
    d1 = (np.log(S/K) + (r - q + 0.5*sigma**2)*T) / (sigma*np.sqrt(T))
    return np.exp(-q*T) * norm.pdf(d1) / (S * sigma * np.sqrt(T))

Theta (Θ): Change in option price per day (time decay)

def theta_call(S, K, T, r, sigma, q=0):
    d1 = (np.log(S/K) + (r - q + 0.5*sigma**2)*T) / (sigma*np.sqrt(T))
    d2 = d1 - sigma*np.sqrt(T)

    theta = (-S*norm.pdf(d1)*sigma*np.exp(-q*T)/(2*np.sqrt(T))
             - r*K*np.exp(-r*T)*norm.cdf(d2)
             + q*S*norm.cdf(d1)*np.exp(-q*T))

    return theta / 365  # Per day

Vega (ν): Change in option price per 1% change in volatility

def vega(S, K, T, r, sigma, q=0):
    d1 = (np.log(S/K) + (r - q + 0.5*sigma**2)*T) / (sigma*np.sqrt(T))
    return S * np.exp(-q*T) * norm.pdf(d1) * np.sqrt(T) / 100  # Per 1%

Rho (ρ): Change in option price per 1% change in interest rate

def rho_call(S, K, T, r, sigma, q=0):
    d2 = (np.log(S/K) + (r - q + 0.5*sigma**2)*T) / (sigma*np.sqrt(T)) - sigma*np.sqrt(T)
    return K * T * np.exp(-r*T) * norm.cdf(d2) / 100  # Per 1%

Position Greeks:

For a strategy with multiple legs, sum Greeks across all legs:

# Example: Bull Call Spread
# Long 1x $180 call
# Short 1x $185 call

delta_position = (1 * delta_long) + (-1 * delta_short)
gamma_position = (1 * gamma_long) + (-1 * gamma_short)
theta_position = (1 * theta_long) + (-1 * theta_short)
vega_position = (1 * vega_long) + (-1 * vega_short)

Greeks Interpretation:

Step 5: Simulate Strategy P/L

Objective: Calculate profit/loss at various stock prices at expiration.

Method:

Generate stock price range (e.g., ±30% from current price):

current_price = 180
price_range = np.linspace(current_price * 0.7, current_price * 1.3, 100)

For each price point, calculate P/L:

def calculate_pnl(strategy, stock_price_at_expiration):
    pnl = 0

    for leg in strategy.legs:
        if leg.type == 'call':
            intrinsic_value = max(0, stock_price_at_expiration - leg.strike)
        else:  # put
            intrinsic_value = max(0, leg.strike - stock_price_at_expiration)

        if leg.position == 'long':
            pnl += (intrinsic_value - leg.premium_paid) * 100  # Per contract
        else:  # short
            pnl += (leg.premium_received - intrinsic_value) * 100

    return pnl * num_contracts

Key Metrics:

• Max Profit: Highest possible P/L
• Max Loss: Worst possible P/L
• Breakeven Point(s): Stock price(s) where P/L = 0
• Profit Probability: Percentage of price range that's profitable (simplified)

Example Output:

Bull Call Spread: $180/$185 on AAPL (30 DTE, 10 contracts)

Current Price: $180.00
Net Debit: $2.50 per spread ($2,500 total)

Max Profit: $2,500 (at $185+)
Max Loss: -$2,500 (at $180-)
Breakeven: $182.50
Risk/Reward: 1:1

Probability Profit: ~55% (if stock stays above $182.50)

Step 6: Generate P/L Diagram (ASCII Art)

Visual representation of P/L across stock prices:

def generate_pnl_diagram(price_range, pnl_values, current_price, width=60, height=15):
    """Generate ASCII P/L diagram"""

    # Normalize to chart dimensions
    max_pnl = max(pnl_values)
    min_pnl = min(pnl_values)

    lines = []
    lines.append(f"\nP/L Diagram: {strategy_name}")
    lines.append("-" * width)

    # Y-axis levels
    levels = np.linspace(max_pnl, min_pnl, height)

    for level in levels:
        if abs(level) < (max_pnl - min_pnl) * 0.05:
            label = f"    0 |"  # Zero line
        else:
            label = f"{level:6.0f} |"

        row = label
        for i in range(width - len(label)):
            idx = int(i / (width - len(label)) * len(price_range))
            pnl = pnl_values[idx]
            price = price_range[idx]

            # Determine character
            if abs(pnl - level) < (max_pnl - min_pnl) / height:
                if pnl > 0:
                    char = '█'  # Profit
                elif pnl < 0:
                    char = '░'  # Loss
                else:
                    char = '─'  # Breakeven
            elif abs(level) < (max_pnl - min_pnl) * 0.05:
                char = '─'  # Zero line
            elif abs(price - current_price) < (price_range[-1] - price_range[0]) * 0.02:
                char = '│'  # Current price line
            else:
                char = ' '

            row += char

        lines.append(row)

    lines.append(" " * 6 + "|" + "-" * (width - 6))
    lines.append(" " * 6 + f"${price_range[0]:.0f}" + " " * (width - 20) + f"${price_range[-1]:.0f}")
    lines.append(" " * (width // 2 - 5) + "Stock Price")

    return "\n".join(lines)

Example Output:

P/L Diagram: Bull Call Spread $180/$185
------------------------------------------------------------
 +2500 |                               ████████████████████
       |                         ██████
       |                   ██████
       |             ██████
     0 |       ──────
       | ░░░░░░
       |░░░░░░
 -2500 |░░░░░
      |____________________________________________________________
       $126                  $180                   $234
                          Stock Price

Legend: █ Profit  ░ Loss  ── Breakeven  │ Current Price

Step 7: Strategy-Specific Analysis

Provide tailored guidance based on strategy type:

Covered Call:

Income Strategy: Generate premium while capping upside

Setup:
- Own 100 shares of AAPL @ $180
- Sell 1x $185 call (30 DTE) for $3.50

Max Profit: $850 (Stock at $185+ = $5 stock gain + $3.50 premium)
Max Loss: Unlimited downside (stock ownership)
Breakeven: $176.50 (Cost basis - premium received)

Greeks:
- Delta: -0.30 (reduces stock delta from 1.00 to 0.70)
- Theta: +$8/day (time decay benefit)

Assignment Risk: If AAPL > $185 at expiration, shares called away

When to Use:
- Neutral to slightly bullish
- Want income in sideways market
- Willing to sell stock at $185

Exit Plan:
- Buy back call if stock rallies strongly (preserve upside)
- Let expire if stock stays below $185
- Roll to next month if want to keep shares

Protective Put:

Insurance Strategy: Limit downside while keeping upside

Setup:
- Own 100 shares of AAPL @ $180
- Buy 1x $175 put (30 DTE) for $2.00

Max Profit: Unlimited (stock can rise infinitely)
Max Loss: -$7 per share = ($5 stock loss + $2 premium)
Breakeven: $182 (Cost basis + premium paid)

Greeks:
- Delta: +0.80 (stock delta 1.00 - put delta 0.20)
- Theta: -$6/day (time decay cost)

Protection: Guaranteed to sell at $175, no matter how far stock falls

When to Use:
- Own stock, worried about short-term drop
- Earnings coming up, want protection
- Alternative to stop-loss (can't be stopped out)

Cost: "Insurance premium" - typically 1-3% of stock value

Exit Plan:
- Let expire worthless if stock rises (cost of insurance)
- Exercise put if stock falls below $175
- Sell put if stock drops but want to keep shares

Iron Condor:

Range-Bound Strategy: Profit from low volatility

Setup (example on AAPL @ $180):
- Sell $175 put for $1.50
- Buy $170 put for $0.50
- Sell $185 call for $1.50
- Buy $190 call for $0.50

Net Credit: $2.00 ($200 per iron condor)

Max Profit: $200 (if stock stays between $175-$185)
Max Loss: $300 (if stock moves outside $170-$190)
Breakevens: $173 and $187
Profit Range: $175 to $185 (58% probability)

Greeks:
- Delta: ~0 (market neutral)
- Theta: +$15/day (time decay benefit)
- Vega: -$25 (short volatility)

When to Use:
- Expect low volatility, range-bound movement
- After big move, think consolidation
- High IV environment (sell expensive options)

Risk: Unlimited if one side tested
- Use stop loss at 2x credit received (exit at -$400)

Adjustments:
- If tested on one side, roll that side out in time
- Close early at 50% max profit to reduce tail risk

Step 8: Earnings Strategy Analysis

Integration with Earnings Calendar:

When user asks about earnings strategies, fetch earnings date:

from earnings_calendar import get_next_earnings_date

earnings_date = get_next_earnings_date("AAPL")
days_to_earnings = (earnings_date - today).days

Pre-Earnings Strategies:

Long Straddle/Strangle:

Setup (AAPL @ $180, earnings in 7 days):
- Buy $180 call for $5.00
- Buy $180 put for $4.50
- Total Cost: $9.50

Thesis: Expect big move (>5%) but unsure of direction

Breakevens: $170.50 and $189.50
Profit if: Stock moves >$9.50 in either direction

Greeks:
- Delta: ~0 (neutral)
- Vega: +$50 (long volatility)
- Theta: -$25/day (time decay hurts)

IV Crush Risk: ⚠️ CRITICAL
- Pre-earnings IV: 40% (elevated)
- Post-earnings IV: 25% (typical)
- IV drop: -15 points = -$750 loss even if stock doesn't move!

Analysis:
- Implied Move: √(DTE/365) × IV × Stock Price
  = √(7/365) × 0.40 × 180 = ±$10.50
- Breakeven Move Needed: ±$9.50
- Probability Profit: ~30-40% (implied move > breakeven move)

Recommendation:
✅ Consider if you expect >10% move (larger than implied)
❌ Avoid if expect normal ~5% earnings move (IV crush will hurt)

Alternative: Buy further OTM strikes to reduce cost
- $175/$185 strangle cost $4.00 (need >$8 move, but cheaper)

Short Iron Condor:

Setup (AAPL @ $180, earnings in 7 days):
- Sell $170/$175 put spread for $2.00
- Sell $185/$190 call spread for $2.00
- Net Credit: $4.00

Thesis: Expect stock to stay range-bound ($175-$185)

Profit Zone: $175 to $185
Max Profit: $400
Max Loss: $100

IV Crush Benefit: ✅
- Short high IV before earnings
- IV drops after earnings → profit on vega
- Even if stock moves slightly, IV drop helps

Greeks:
- Delta: ~0 (market neutral)
- Vega: -$40 (short volatility - good here!)
- Theta: +$20/day

Recommendation:
✅ Good if expect normal earnings reaction (<8% move)
✅ Benefit from IV crush regardless of direction
⚠️ Risk if stock gaps outside range (>10% move)

Exit Plan:
- Close next day if IV crushed (capture profit early)
- Use stop loss if one side tested (-2x credit)

Step 9: Risk Management Guidance

Position Sizing:

Account Size: $50,000
Risk Tolerance: 2% per trade = $1,000 max risk

Iron Condor Example:
- Max loss per spread: $300
- Max contracts: $1,000 / $300 = 3 contracts
- Actual position: 3 iron condors

Bull Call Spread Example:
- Debit paid: $2.50 per spread
- Max contracts: $1,000 / $250 = 4 contracts
- Actual position: 4 spreads

Portfolio Greeks Management:

Portfolio Guidelines:
- Delta: -10 to +10 (mostly neutral)
- Theta: Positive preferred (seller advantage)
- Vega: Monitor if >$500 (IV risk)

Current Portfolio:
- Delta: +5 (slightly bullish)
- Theta: +$150/day (collecting $150 daily)
- Vega: -$300 (short volatility)

Interpretation:
✅ Neutral delta (safe)
✅ Positive theta (time working for you)
⚠️ Short vega: If IV spikes, lose $300 per 1% IV increase
→ Reduce short premium positions if VIX rising

Adjustments and Exits:

Exit Rules by Strategy:

Covered Call:
- Profit: 50-75% of max profit
- Loss: Stock drops >5%, buy back call to preserve upside
- Time: 7-10 DTE, roll to avoid assignment

Spreads:
- Profit: 50% of max profit (close early, reduce tail risk)
- Loss: 2x debit paid (cut losses early)
- Time: 21 DTE, close or roll (avoid gamma risk)

Iron Condor:
- Profit: 50% of credit (close early common)
- Loss: One side tested, 2x credit lost
- Adjustment: Roll tested side out in time

Straddle/Strangle:
- Profit: Stock moved >breakeven, close immediately
- Loss: Theta eating position, stock not moving
- Time: Day after earnings (if earnings play)

Output Format

Strategy Analysis Report Template:

# Options Strategy Analysis: [Strategy Name]

**Symbol:** [TICKER]
**Strategy:** [Strategy Type]
**Expiration:** [Date] ([DTE] days)
**Contracts:** [Number]

---

## Strategy Setup

### Leg Details
| Leg | Type | Strike | Price | Position | Quantity |
|-----|------|--------|-------|----------|----------|
| 1 | Call | $180 | $5.00 | Long | 1 |
| 2 | Call | $185 | $2.50 | Short | 1 |

**Net Debit/Credit:** $2.50 debit ($250 total for 1 spread)

---

## Profit/Loss Analysis

**Max Profit:** $250 (at $185+)
**Max Loss:** -$250 (at $180-)
**Breakeven:** $182.50
**Risk/Reward Ratio:** 1:1

**Probability Analysis:**
- Probability of Profit: ~55% (stock above $182.50)
- Expected Value: $25 (simplified)

---

## P/L Diagram

[ASCII art diagram here]

---

## Greeks Analysis

### Position Greeks (1 spread)
- **Delta:** +0.20 (gains $20 if stock +$1)
- **Gamma:** +0.03 (delta increases by 0.03 if stock +$1)
- **Theta:** -$5/day (loses $5 per day from time decay)
- **Vega:** +$8 (gains $8 if IV increases 1%)

### Interpretation
- **Directional Bias:** Slightly bullish (positive delta)
- **Time Decay:** Working against you (negative theta)
- **Volatility:** Benefits from IV increase (positive vega)

---

## Risk Assessment

### Maximum Risk
**Scenario:** Stock falls below $180
**Max Loss:** -$250 (100% of premium paid)
**% of Account:** 0.5% (if $50k account)

### Assignment Risk
**Early Assignment:** Low (calls have time value)
**At Expiration:** Manage positions if in-the-money

---

## Trade Management

### Entry
✅ Enter if: [Conditions]
- Stock price $178-$182
- IV below 30%
- >21 DTE

### Profit Taking
- **Target 1:** 50% profit ($125) - Close half
- **Target 2:** 75% profit ($187.50) - Close all

### Stop Loss
- **Trigger:** Stock falls below $177 (-$150 loss)
- **Action:** Close position immediately

### Adjustments
- If stock rallies to $184, consider rolling short call higher
- If stock drops to $179, add second spread at $175/$180

---

## Suitability

### When to Use This Strategy
✅ Moderately bullish on AAPL
✅ Expect upside to $185-$190
✅ Want defined risk
✅ 21-45 DTE timeframe

### When to Avoid
❌ Very bullish (buy stock or long call instead)
❌ High IV environment (wait for IV to drop)
❌ Earnings in <7 days (IV crush risk)

---

## Alternatives Comparison

| Strategy | Max Profit | Max Loss | Complexity | When Better |
|----------|-----------|----------|------------|-------------|
| Bull Call Spread | $250 | -$250 | Medium | Moderately bullish |
| Long Call | Unlimited | -$500 | Low | Very bullish |
| Covered Call | $850 | Unlimited | Medium | Own stock already |
| Bull Put Spread | $300 | -$200 | Medium | Want credit spread |

**Recommendation:** Bull call spread is good balance of risk/reward for moderate bullish thesis.

---

*Disclaimer: This is theoretical analysis using Black-Scholes pricing. Actual market prices may differ. Trade at your own risk. Options are complex instruments with significant loss potential.*

File Naming Convention:

options_analysis_[TICKER]_[STRATEGY]_[DATE].md

Example: options_analysis_AAPL_BullCallSpread_2025-11-08.md

Key Principles

Theoretical Pricing Limitations

What Users Should Know: 1. Black-Scholes Assumptions:

• European-style options (can't exercise early)
• Constant volatility (IV changes in reality)
• No transaction costs
• Continuous trading

2. Real vs Theoretical:

• Bid-ask spread: Actual cost higher than theoretical
• American options: Can be exercised early (especially ITM puts)
• Liquidity: Wide markets on illiquid options
• Dividends: Ex-dividend dates affect pricing

3. Best Practices:

• Use as educational tool and comparative analysis
• Get real quotes from broker before trading
• Understand theoretical price ≈ mid-market price
• Account for commissions and slippage

Volatility Guidance

Historical vs Implied Volatility:

Historical Volatility (HV): What happened
- Calculated from past price movements
- Objective, based on data
- Available for free (FMP API)

Implied Volatility (IV): What market expects
- Derived from option prices
- Subjective, based on supply/demand
- Requires live options data (user provides)

Comparison:
- IV > HV: Options expensive (consider selling)
- IV < HV: Options cheap (consider buying)
- IV = HV: Fairly priced

IV Percentile:

User provides current IV, we calculate percentile:

# Fetch 1-year HV data
historical_hvs = calculate_hv_series(prices_1yr, window=30)

# Calculate IV percentile
iv_percentile = percentileofscore(historical_hvs, current_iv)

if iv_percentile > 75:
    guidance = "High IV - consider selling premium (credit spreads, iron condors)"
elif iv_percentile < 25:
    guidance = "Low IV - consider buying options (long calls/puts, debit spreads)"
else:
    guidance = "Normal IV - any strategy appropriate"

Integration with Other Skills

Earnings Calendar:

• Fetch earnings dates automatically
• Suggest earnings-specific strategies
• Calculate days to earnings (DTE critical for IV)
• Warn about IV crush risk

Technical Analyst:

• Use support/resistance for strike selection
• Trend analysis for directional strategies
• Breakout potential for straddle/strangle timing

US Stock Analysis:

• Fundamental analysis for longer-term strategies (LEAPS)
• Dividend yield for covered call/put analysis
• Earnings quality for earnings plays

Bubble Detector:

• High bubble risk → focus on protective puts
• Low risk → bullish strategies
• Critical risk → avoid long premium (theta hurts)

Portfolio Manager:

• Track options positions alongside stock positions
• Aggregate Greeks across portfolio
• Options as hedging tool for stock positions

Important Notes

• All analysis in English
• Educational focus: Strategies explained clearly
• Theoretical pricing: Black-Scholes approximation
• User IV input: Optional, defaults to HV
• No real-time data required: FMP Free tier sufficient
• Dependencies: Python 3.9+, numpy, scipy, requests

Common Use Cases

Use Case 1: Learn Strategy

User: "Explain a covered call"

Workflow:
1. Load strategy reference (references/strategies_guide.md)
2. Explain concept, risk/reward, when to use
3. Simulate example on AAPL
4. Show P/L diagram
5. Compare to alternatives

Use Case 2: Analyze Specific Trade

User: "Analyze $180/$185 bull call spread on AAPL, 30 days"

Workflow:
1. Fetch AAPL price from FMP
2. Calculate HV or ask user for IV
3. Price both options (Black-Scholes)
4. Calculate Greeks
5. Simulate P/L
6. Generate analysis report

Use Case 3: Earnings Strategy

User: "Should I trade options before NVDA earnings?"

Workflow:
1. Fetch NVDA earnings date (Earnings Calendar)
2. Calculate days to earnings
3. Estimate IV percentile (if user provides IV)
4. Suggest straddle/strangle vs iron condor
5. Warn about IV crush
6. Simulate both strategies

Use Case 4: Portfolio Greeks Check

User: "What are my total portfolio Greeks?"

Workflow:
1. User provides current positions
2. Calculate Greeks for each position
3. Sum Greeks across portfolio
4. Assess overall exposure
5. Suggest adjustments if needed

Troubleshooting

Problem: IV not available

• Solution: Use HV as proxy, note to user
• Ask user to provide IV from broker platform

Problem: Negative option price

• Solution: Check inputs (strike vs stock price)
• Deep ITM options may have numerical issues

Problem: Greeks seem wrong

• Solution: Verify inputs (T, sigma, r)
• Check if using annual vs daily values

Problem: Strategy too complex

• Solution: Break into legs, analyze separately
• Refer to references for strategy details

Resources

References:

• references/black_scholes_methodology.md - Black-Scholes formulas, Greeks, and interpretation
• references/strategies_guide.md - All 17+ strategies explained (future)
• references/greeks_explained.md - Greeks deep dive (future)
• references/volatility_guide.md - HV vs IV, when to trade (future)

Scripts:

• scripts/black_scholes.py - Pricing engine and Greeks
• scripts/strategy_analyzer.py - Strategy simulation
• scripts/earnings_strategy.py - Earnings-specific analysis

External Resources:

• Options Playbook: https://www.optionsplaybook.com/
• CBOE Education: https://www.cboe.com/education/
• Black-Scholes Calculator: Various online tools for verification

---

Version: 1.0 Last Updated: 2025-11-08 Dependencies: Python 3.9+, numpy, scipy, requests API: FMP API (Free tier sufficient)

Options Strategy Advisor

Educational options trading tool providing theoretical pricing, strategy analysis, and risk management guidance using Black-Scholes model.

Overview

Options Strategy Advisor helps traders understand and analyze options strategies without requiring expensive real-time options data. It uses theoretical pricing models (Black-Scholes) combined with free stock market data (FMP API) to simulate strategies and calculate Greeks.

Key Features:

• ✅ Black-Scholes pricing engine
• ✅ All Greeks calculation (Delta, Gamma, Theta, Vega, Rho)
• ✅ 17+ options strategies supported
• ✅ P/L simulation and visualization
• ✅ Earnings strategy integration
• ✅ Historical volatility calculation
• ✅ Risk management guidance

Why This Approach?

No expensive data subscriptions needed:

• Real-time options data: $99-$500/month (Polygon.io, Intrinio)
• FMP API Free tier: $0/month (250 requests/day)

Educational focus:

• Learn how strategies work
• Understand Greeks and risk metrics
• Compare strategies side-by-side

Practical application:

• Theoretical prices ≈ market mid-prices
• User can input actual IV from broker
• Good for strategy planning and education

Supported Strategies

Income Strategies

1. Covered Call - Generate income from stock holdings 2. Cash-Secured Put - Get paid to buy stock 3. Poor Man's Covered Call - Capital-efficient covered call

Protection Strategies

4. Protective Put - Insurance for stock positions 5. Collar - Limited risk/reward protection

Directional Strategies

6. Bull Call Spread - Limited risk bullish play 7. Bull Put Spread - Credit spread for bullish view 8. Bear Call Spread - Credit spread for bearish view 9. Bear Put Spread - Limited risk bearish play

Volatility Strategies

10. Long Straddle - Profit from big moves 11. Long Strangle - Cheaper straddle, bigger move needed 12. Short Straddle - Profit from no movement (high risk) 13. Short Strangle - Wider range straddle

Range-Bound Strategies

14. Iron Condor - Profit from range-bound trading 15. Iron Butterfly - Tight range profit

Advanced Strategies

16. Calendar Spread - Time decay play 17. Diagonal Spread - Directional + time decay

Installation

Prerequisites

• Python 3.8+
• FMP API key (free tier sufficient)

Install Dependencies

pip install numpy scipy requests pandas

Get FMP API Key

1. Visit https://financialmodelingprep.com/developer/docs 2. Sign up for free account 3. Copy API key 4. Set environment variable:

export FMP_API_KEY="your_key_here"

Quick Start

Test Black-Scholes Pricer

python scripts/black_scholes.py

Example Output:

BLACK-SCHOLES OPTIONS PRICER - EXAMPLE
======================================================================

Input Parameters:
  Stock Price: $180.00
  Strike Price: $185.00
  Days to Expiration: 30
  Volatility: 25.0%
  Risk-Free Rate: 5.30%
  Dividend Yield: 1.0%

======================================================================
CALL OPTION
======================================================================
Price: $2.45
Intrinsic Value: $0.00
Time Value: $2.45

Greeks:
  Delta: 0.3654 ($36.54 per $1 move)
  Gamma: 0.0234 (delta changes by 0.0234)
  Theta: -$0.18/day (loses $0.18 per day)
  Vega: $0.25 per 1% IV (gains $0.25 if IV +1%)
  Rho: $0.12 per 1% rate (gains $0.12 if rate +1%)

Use in Your Code

from scripts.black_scholes import OptionPricer

# Initialize pricer
pricer = OptionPricer(
    S=180,          # Stock price
    K=185,          # Strike price
    T=30/365,       # Time to expiration (years)
    r=0.053,        # Risk-free rate (5.3%)
    sigma=0.25,     # Volatility (25%)
    q=0.01          # Dividend yield (1%)
)

# Get call option price
call_price = pricer.call_price()
print(f"Call Price: ${call_price:.2f}")

# Get all Greeks for call
call_greeks = pricer.get_all_greeks('call')
print(f"Delta: {call_greeks['delta']:.4f}")
print(f"Gamma: {call_greeks['gamma']:.4f}")
print(f"Theta: ${call_greeks['theta']:.2f}/day")
print(f"Vega: ${call_greeks['vega']:.2f} per 1%")

Calculate Historical Volatility

from scripts.black_scholes import (
    calculate_historical_volatility,
    fetch_historical_prices_for_hv
)

# Fetch prices from FMP
api_key = "your_key"
prices = fetch_historical_prices_for_hv("AAPL", api_key, days=90)

# Calculate 30-day HV
hv = calculate_historical_volatility(prices, window=30)
print(f"30-Day HV: {hv*100:.2f}%")

Understanding the Metrics

Option Price Components

Intrinsic Value:

• Call: max(0, Stock Price - Strike Price)
• Put: max(0, Strike Price - Stock Price)

Time Value:

• Option Price - Intrinsic Value
• Decays to $0 at expiration

The Greeks

Delta (Δ) - Directional Exposure

Range: 0 to 1 (calls), -1 to 0 (puts)
Meaning: Change in option price per $1 stock move

Example: Δ = 0.50
→ If stock +$1, option +$0.50
→ If stock -$1, option -$0.50

Gamma (Γ) - Delta Acceleration

Meaning: Change in delta per $1 stock move
Peak: ATM options
Low: Deep ITM or OTM

Example: Γ = 0.05, Δ currently = 0.50
→ If stock +$1, delta becomes 0.55

Theta (Θ) - Time Decay

Meaning: Change in option price per day
Sign: Usually negative (options lose value over time)
Peak: Last 30 days before expiration

Example: Θ = -$0.15/day
→ Tomorrow, option loses $0.15 if nothing else changes

Vega (ν) - Volatility Sensitivity

Meaning: Change in option price per 1% IV change
Sign: Always positive (options gain value when vol increases)

Example: ν = $0.25 per 1%
→ If IV increases from 25% to 26%, option +$0.25

Rho (ρ) - Interest Rate Sensitivity

Meaning: Change in option price per 1% rate change
Sign: Positive for calls, negative for puts
Impact: Usually small unless long-dated options

Example: ρ = $0.10 per 1%
→ If interest rate increases 1%, option +$0.10

Volatility: HV vs IV

Historical Volatility (HV):

• Calculated from past price movements
• Objective, based on actual data
• Available free (from price data)

Implied Volatility (IV):

• Derived from option market prices
• Subjective, based on supply/demand
• Requires real-time options data (or user input)

Comparison:

IV > HV: Options expensive → Consider selling premium
IV < HV: Options cheap → Consider buying options
IV = HV: Fairly priced → Any strategy works

Common Workflows

1. Analyze a Strategy

from scripts.black_scholes import OptionPricer

# Stock: AAPL @ $180
# Strategy: Bull Call Spread $180/$185 (30 DTE)

# Price long call ($180 strike)
long_call = OptionPricer(S=180, K=180, T=30/365, r=0.053, sigma=0.25)
long_price = long_call.call_price()
long_delta = long_call.call_delta()

# Price short call ($185 strike)
short_call = OptionPricer(S=180, K=185, T=30/365, r=0.053, sigma=0.25)
short_price = short_call.call_price()
short_delta = short_call.call_delta()

# Strategy metrics
net_debit = long_price - short_price
max_profit = (185 - 180) - net_debit
max_loss = -net_debit
position_delta = long_delta - short_delta

print(f"Bull Call Spread $180/$185")
print(f"Net Debit: ${net_debit:.2f}")
print(f"Max Profit: ${max_profit:.2f} (at $185+)")
print(f"Max Loss: ${max_loss:.2f} (at $180-)")
print(f"Position Delta: {position_delta:.4f}")

2. Compare IV to HV

# Get HV
prices = fetch_historical_prices_for_hv("AAPL", api_key, days=90)
hv = calculate_historical_volatility(prices, window=30)

# User provides IV (from broker platform)
iv = 0.28  # 28% from ThinkorSwim

print(f"Historical Volatility: {hv*100:.2f}%")
print(f"Implied Volatility: {iv*100:.1f}%")

if iv > hv * 1.1:
    print("→ Options expensive (IV > HV) - Consider selling premium")
elif iv < hv * 0.9:
    print("→ Options cheap (IV < HV) - Consider buying options")
else:
    print("→ Fairly priced")

3. Earnings Strategy

Check if earnings coming up (use Earnings Calendar skill):

# If earnings in 7 days:
# - IV typically elevated (30-50% higher)
# - Consider straddle/strangle (profit from big move)
# - Or sell iron condor (profit from IV crush)

# Example: Long Straddle
straddle_cost = call_price + put_price
breakeven_up = stock_price + straddle_cost
breakeven_down = stock_price - straddle_cost

print(f"Straddle Cost: ${straddle_cost:.2f}")
print(f"Breakevens: ${breakeven_down:.2f} / ${breakeven_up:.2f}")
print(f"Need {abs(breakeven_up - stock_price)/stock_price*100:.1f}% move to profit")

Limitations & Best Practices

Theoretical vs Market Prices

Black-Scholes Assumptions:

• European options (can't exercise early)
• Constant volatility (changes in reality)
• No transaction costs
• Continuous trading

Real World Differences:

• American options (most stocks) can exercise early
• Bid-ask spread: Actual cost higher than theoretical mid
• Commissions and slippage
• Liquidity: Wide markets on illiquid options

Best Practices

1. Use for Education & Planning:

• Learn how strategies work
• Compare different approaches
• Understand risk/reward before trading

2. Verify Before Trading:

• Get real quotes from your broker
• Check bid-ask spread
• Confirm option liquidity (open interest, volume)

3. Input Actual IV:

• Theoretical price assumes constant volatility
• Use current market IV for accuracy
• Check IV percentile (high/low relative to history)

4. Account for Dividends:

• Ex-dividend dates affect option prices
• Calls lose value, puts gain value on ex-div date
• Script supports dividend yield input

5. Monitor Greeks:

• Delta: Overall directional exposure
• Theta: Daily time decay (seller advantage)
• Vega: Volatility risk (watch during earnings)
• Gamma: Risk of delta changing (avoid near expiration)

Integration with Other Skills

Earnings Calendar:

• Fetch earnings dates
• Identify IV crush opportunities
• Time earnings strategies

Technical Analyst:

• Use support/resistance for strike selection
• Trend analysis for directional strategies
• Breakout potential for straddle timing

US Stock Analysis:

• Fundamental analysis for LEAPS
• Dividend yield for covered call/put
• Earnings quality for earnings plays

Bubble Detector:

• High risk → protective puts
• Low risk → bullish strategies
• Critical risk → avoid long premium

Portfolio Manager:

• Track options with stock positions
• Aggregate Greeks across portfolio
• Options as hedging tool

API Usage & Costs

Free Tier Sufficient:

• Stock prices: 1 request per symbol
• Historical prices (HV): 1 request per symbol
• Dividend data: 1 request per symbol

Example Analysis Cost:

Covered Call on AAPL:
- Current price: 1 request
- HV calculation: 1 request (90 days data)
- Dividend yield: 1 request
Total: 3 requests

Daily budget: 250 requests / day
→ Can analyze ~80 strategies per day

Troubleshooting

Negative Option Price

Cause: Invalid inputs (strike vs stock price) Solution: Check that inputs make sense

Greeks Seem Wrong

Cause: Using wrong units (annual vs daily) Solution: Verify T is in years, theta is per day

HV Very Different from IV

Normal: IV reflects future expectations, HV is past Action: Use IV from broker for more accuracy

Option Price Too High/Low

Cause: Volatility input incorrect Solution: Verify sigma is annual (e.g., 0.25 for 25%)

Resources

Documentation

• SKILL.md - Complete workflow and strategies
• references/strategies_guide.md - All strategies explained (TBD)
• references/greeks_explained.md - Greeks deep dive (TBD)

External Resources

• Options Playbook: https://www.optionsplaybook.com/
• CBOE Education: https://www.cboe.com/education/
• Black-Scholes Calculator: https://www.option-price.com/

Get Real IV

• ThinkorSwim (TD Ameritrade): Free
• TastyTrade: Free
• Barchart: https://www.barchart.com/options
• CBOE: http://www.cboe.com/delayedquote/

Future Enhancements

Planned:

• Strategy simulation script (complete P/L analysis)
• P/L diagram generator (ASCII art)
• Earnings strategy advisor (integrated with Earnings Calendar)
• Complete strategy reference guides

Contributions Welcome:

• Additional strategies
• Improved volatility models
• Better visualization tools

License

Educational use. Trade at your own risk. Options involve significant risk and are not suitable for all investors.

---

Version: 1.0 Last Updated: 2025-11-08 Dependencies: Python 3.8+, numpy, scipy, requests API: FMP API (Free tier sufficient) Model: Black-Scholes (European options pricing)

Black-Scholes Methodology Reference

Overview

The Black-Scholes model is the foundation for theoretical options pricing in this skill. This document provides the mathematical framework and interpretation guidance.

Black-Scholes Formula

Call Option Price

C = S × e^(-qT) × N(d₁) - K × e^(-rT) × N(d₂)

Put Option Price

P = K × e^(-rT) × N(-d₂) - S × e^(-qT) × N(-d₁)

Parameters

d₁ and d₂ Calculations

d₁ = [ln(S/K) + (r - q + σ²/2) × T] / (σ × √T)
d₂ = d₁ - σ × √T

The Greeks

Delta (Δ)

• Definition: Price change per $1 move in underlying
• Call: 0 to +1 (positive, bullish)
• Put: -1 to 0 (negative, bearish)
• ATM options: ~0.50 (call) or ~-0.50 (put)

Gamma (Γ)

• Definition: Rate of change of delta
• Always positive for long options
• Highest at ATM, decreases as option moves ITM/OTM
• Increases as expiration approaches

Theta (Θ)

• Definition: Daily time decay ($/day)
• Negative for long options (lose value daily)
• Positive for short options (collect decay)
• Accelerates in final 30 days

Vega (ν)

• Definition: Price change per 1% IV move
• Always positive for long options
• Highest at ATM
• Critical for earnings plays

Rho (ρ)

• Definition: Price change per 1% rate change
• Positive for calls, negative for puts
• Small impact in short-dated options

Historical vs Implied Volatility

IV-HV Relationship

• IV > HV: Options expensive → consider selling premium
• IV < HV: Options cheap → consider buying
• IV ≈ HV: Fairly priced

IV Percentile Interpretation

Model Limitations

Assumptions (Not Always True)

1. Constant volatility - IV changes constantly 2. European exercise - American options can exercise early 3. No transaction costs - Commissions and slippage exist 4. Continuous trading - Gaps and halts occur 5. Log-normal distribution - Fat tails exist in practice

When Model Underperforms

• Deep ITM American puts (early exercise value)
• Near expiration with high gamma
• Earnings/events (IV regime change)
• Low liquidity options (wide bid-ask)

Practical Adjustments

American Options

• Calls: Black-Scholes accurate if no dividends
• Puts: May undervalue ITM puts near expiration
• Solution: Note "European pricing approximation"

Dividend Handling

• Include dividend yield (q) in calculations
• For discrete dividends: subtract PV from stock price
• Ex-dividend dates affect early exercise decisions

Strategy Selection Framework

By Market Outlook

By Volatility View

Position Sizing Guidelines

Risk-Based Sizing

Max Contracts = (Account Risk $) / (Max Loss per Contract)

Portfolio Greeks Limits

References

• Black, F. & Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities"
• Hull, J.C. "Options, Futures, and Other Derivatives"
• CBOE Education: https://www.cboe.com/education/