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options-strategy-advisor by nicepkg/ai-workflow
npx skills add https://github.com/nicepkg/ai-workflow --skill options-strategy-advisor此技能使用理论定价模型提供全面的期权策略分析和教育。它帮助交易者理解、分析和模拟期权策略,无需实时市场数据订阅。
核心能力:
数据来源:
在以下情况使用此技能:
示例请求:
广告位招租
在这里展示您的产品或服务
触达数万 AI 开发者,精准高效
用户需提供:
用户可选提供:
从 FMP API 获取:
示例用户输入:
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)
目标: 根据历史价格变动估算波动率。
方法:
# 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
输出:
用户可以覆盖:
--iv 28.0 参数Black-Scholes 模型:
对于欧式期权:
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
调整:
Python 实现:
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
每个期权腿的输出:
希腊值衡量期权价格对各种因素的敏感性:
Delta (Δ): 股票价格每变动 $1,期权价格的变化
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): 股票价格每变动 $1,Delta 的变化
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): 期权价格每天的变化(时间衰减)
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): 波动率每变化 1%,期权价格的变化
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): 利率每变化 1%,期权价格的变化
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%
头寸希腊值:
对于有多条腿的策略,将所有腿的希腊值求和:
# 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)
希腊值解读:
| 希腊值 | 含义 | 示例 |
|---|---|---|
| Delta | 方向性敞口 | Δ = 0.50 → 如果股票 +$1,盈利 $50 |
| Gamma | Delta 加速度 | Γ = 0.05 → 如果股票 +$1,Delta 增加 0.05 |
| Theta | 每日时间衰减 | Θ = -$5 → 每天因时间流逝损失 $5 |
| Vega | 波动率敏感性 | ν = $10 → 如果 IV 增加 1%,盈利 $10 |
| Rho | 利率敏感性 | ρ = $2 → 如果利率增加 1%,盈利 $2 |
目标: 计算到期时不同股票价格下的盈亏。
方法:
生成股票价格范围(例如,从当前价格 ±30%):
current_price = 180
price_range = np.linspace(current_price * 0.7, current_price * 1.3, 100)
对于每个价格点,计算盈亏:
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
关键指标:
示例输出:
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 $182.50)
盈亏随股票价格变化的可视化表示:
def generate_pnl_diagram(price_range, pnl_values, current_price, width=60, height=15):
"""Generate ASCII P/L diagram"""
# Normalize to chart dimensions
max_pnl = max(pnl_values)
min_pnl = min(pnl_values)
lines = []
lines.append(f"\nP/L Diagram: {strategy_name}")
lines.append("-" * width)
# Y-axis levels
levels = np.linspace(max_pnl, min_pnl, height)
for level in levels:
if abs(level) < (max_pnl - min_pnl) * 0.05:
label = f" 0 |" # Zero line
else:
label = f"{level:6.0f} |"
row = label
for i in range(width - len(label)):
idx = int(i / (width - len(label)) * len(price_range))
pnl = pnl_values[idx]
price = price_range[idx]
# Determine character
if abs(pnl - level) < (max_pnl - min_pnl) / height:
if pnl > 0:
char = '█' # Profit
elif pnl < 0:
char = '░' # Loss
else:
char = '─' # Breakeven
elif abs(level) < (max_pnl - min_pnl) * 0.05:
char = '─' # Zero line
elif abs(price - current_price) < (price_range[-1] - price_range[0]) * 0.02:
char = '│' # Current price line
else:
char = ' '
row += char
lines.append(row)
lines.append(" " * 6 + "|" + "-" * (width - 6))
lines.append(" " * 6 + f"${price_range[0]:.0f}" + " " * (width - 20) + f"${price_range[-1]:.0f}")
lines.append(" " * (width // 2 - 5) + "Stock Price")
return "\n".join(lines)
示例输出:
P/L Diagram: Bull Call Spread $180/$185
------------------------------------------------------------
+2500 | ████████████████████
| ██████
| ██████
| ██████
0 | ──────
| ░░░░░░
|░░░░░░
-2500 |░░░░░
|____________________________________________________________
$126 $180 $234
Stock Price
Legend: █ Profit ░ Loss ── Breakeven │ Current Price
根据策略类型提供定制指导:
备兑认购:
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
保护性认沽:
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
铁鹰策略:
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
与财报日历集成:
当用户询问财报策略时,获取财报日期:
from earnings_calendar import get_next_earnings_date
earnings_date = get_next_earnings_date("AAPL")
days_to_earnings = (earnings_date - today).days
财报前策略:
买入跨式/宽跨式组合:
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)
卖出铁鹰策略:
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)
头寸规模:
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
投资组合希腊值管理:
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
调整与退出:
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)
策略分析报告模板:
# 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.*
文件命名约定:
options_analysis_[TICKER]_[STRATEGY]_[DATE].md
示例:options_analysis_AAPL_BullCallSpread_2025-11-08.md
用户应了解:
Black-Scholes 假设:
实际 vs 理论:
最佳实践:
历史 vs 隐含波动率:
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 百分位数:
用户提供当前 IV,我们计算百分位数:
# 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"
财报日历:
技术分析师:
美国股票分析:
泡沫检测器:
投资组合经理:
用例 1:学习策略
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
用例 2:分析特定交易
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
用例 3:财报策略
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
用例 4:投资组合希腊值检查
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
问题:IV 不可用
问题:期权价格为负
问题:希腊值看起来不对
问题:策略太复杂
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:
Data Sources:
Use this skill when:
Example requests:
Required from User:
Optional from User:
Fetched from FMP API:
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)
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:
User Can Override:
--iv 28.0 parameterBlack-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:
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:
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:
| 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% |
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:
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 $182.50)
Visual representation of P/L across stock prices:
def generate_pnl_diagram(price_range, pnl_values, current_price, width=60, height=15):
"""Generate ASCII P/L diagram"""
# Normalize to chart dimensions
max_pnl = max(pnl_values)
min_pnl = min(pnl_values)
lines = []
lines.append(f"\nP/L Diagram: {strategy_name}")
lines.append("-" * width)
# Y-axis levels
levels = np.linspace(max_pnl, min_pnl, height)
for level in levels:
if abs(level) < (max_pnl - min_pnl) * 0.05:
label = f" 0 |" # Zero line
else:
label = f"{level:6.0f} |"
row = label
for i in range(width - len(label)):
idx = int(i / (width - len(label)) * len(price_range))
pnl = pnl_values[idx]
price = price_range[idx]
# Determine character
if abs(pnl - level) < (max_pnl - min_pnl) / height:
if pnl > 0:
char = '█' # Profit
elif pnl < 0:
char = '░' # Loss
else:
char = '─' # Breakeven
elif abs(level) < (max_pnl - min_pnl) * 0.05:
char = '─' # Zero line
elif abs(price - current_price) < (price_range[-1] - price_range[0]) * 0.02:
char = '│' # Current price line
else:
char = ' '
row += char
lines.append(row)
lines.append(" " * 6 + "|" + "-" * (width - 6))
lines.append(" " * 6 + f"${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
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
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)
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)
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
What Users Should Know:
Black-Scholes Assumptions:
Real vs Theoretical:
Best Practices:
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"
Earnings Calendar:
Technical Analyst:
US Stock Analysis:
Bubble Detector:
Portfolio Manager:
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
Problem: IV not available
Problem: Negative option price
Problem: Greeks seem wrong
Problem: Strategy too complex
References:
references/strategies_guide.md - All 17+ strategies explainedreferences/greeks_explained.md - Greeks deep divereferences/volatility_guide.md - HV vs IV, when to tradeScripts:
scripts/black_scholes.py - Pricing engine and Greeksscripts/strategy_analyzer.py - Strategy simulationscripts/earnings_strategy.py - Earnings-specific analysisExternal Resources:
Version : 1.0 Last Updated : 2025-11-08 Dependencies : Python 3.8+, numpy, scipy, pandas, requests API : FMP API (Free tier sufficient)
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