---
name: options-strategy-advisor
description: Analyze and simulate options trading strategies using Black-Scholes pricing, Greeks calculation, and risk management guidance.
---

# 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:**
```bash
pip install numpy scipy requests
```

**Quick Start Examples:**
```bash
# 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:**
```python
# 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:**
```python
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
```python
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
```python
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)
```python
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
```python
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
```python
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:
```python
# 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:**

| Greek | Meaning | Example |
|-------|---------|---------|
| **Delta** | Directional exposure | Δ = 0.50 → $50 profit if stock +$1 |
| **Gamma** | Delta acceleration | Γ = 0.05 → Delta increases by 0.05 if stock +$1 |
| **Theta** | Daily time decay | Θ = -$5 → Lose $5/day from time passing |
| **Vega** | Volatility sensitivity | ν = $10 → Gain $10 if IV increases 1% |
| **Rho** | Interest rate sensitivity | ρ = $2 → Gain $2 if rates increase 1% |

### 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):
```python
current_price = 180
price_range = np.linspace(current_price * 0.7, current_price * 1.3, 100)
```

For each price point, calculate P/L:
```python
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:**

```python
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:
```python
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:**

```markdown
# 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:
```python
# 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)