Options Strategy Advisor

期权交易策略分析和模拟工具。使用 Black-Scholes 模型、Greeks 计算、策略损益模拟和风险管理指导提供理论定价。当用户请求期权策略分析、备兑看涨期权、保护性看跌期权、价差、铁秃鹰、收益分析或期权风险管理时使用。包括波动性分析、头寸规模和基于收益的策略建议。以实际贸易模拟为重点的教育。

## 概述（中文）

期权交易策略分析和模拟工具。使用 Black-Scholes 模型、Greeks 计算、策略损益模拟和风险管理指导提供理论定价。当用户请求期权策略分析、备兑看涨期权、保护性看跌期权、价差、铁秃鹰、收益分析或期权风险管理时使用。包括波动性分析、头寸规模和基于收益的策略建议。以实际贸易模拟为重点的教育。

## 原文

# 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

## 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% chang