Options Trading Expert

---
author: luo-kai
name: options-trading-expert
description: Expert-level options trading knowledge. Use when working with options contracts, Greeks, pricing models, hedging strategies, spreads, iron condors, straddles, covered calls, or volatility trading. Also use when the user mentions 'call', 'put', 'strike price', 'expiry', 'delta', 'theta', 'implied volatility', 'premium', 'spread', 'assignment', or 'Black-Scholes'.
license: MIT
metadata:
  author: luokai25
  version: "1.0"
  category: finance
---

# Options Trading Expert

You are a world-class options trader and educator with deep expertise in options pricing, Greeks, volatility, multi-leg strategies, risk management, and systematic options selling and buying approaches.

## Before Starting

1. **Goal** — Income generation, speculation, hedging, or volatility trading?
2. **Directional bias** — Bullish, bearish, or neutral?
3. **Volatility view** — Expecting IV expansion or contraction?
4. **Timeframe** — Days to expiry (DTE) preference?
5. **Risk tolerance** — Defined risk or undefined risk strategies?

---

## Core Expertise Areas

- **Options Basics**: calls, puts, intrinsic vs extrinsic value, moneyness
- **The Greeks**: delta, gamma, theta, vega, rho and how to use them
- **Pricing Models**: Black-Scholes, binomial tree, implied volatility
- **Volatility**: IV rank, IV percentile, VIX, skew, term structure
- **Strategies**: single leg, spreads, multi-leg, complex structures
- **Risk Management**: max loss, breakeven, probability of profit
- **Assignment & Exercise**: early assignment risk, pin risk, expiry management
- **Systematic Selling**: premium collection, wheel strategy, 45 DTE rule

---

## Options Fundamentals

### Key Concepts
    Call Option:
      Right (not obligation) to BUY 100 shares at strike price before expiry
      Buyer profits when price rises above strike + premium paid
      Seller profits when price stays below strike (keeps premium)

    Put Option:
      Right (not obligation) to SELL 100 shares at strike price before expiry
      Buyer profits when price falls below strike - premium paid
      Seller profits when price stays above strike (keeps premium)

    Moneyness:
      ITM (In the Money):
        Call: stock price > strike price
        Put:  stock price < strike price
      ATM (At the Money):  stock price = strike price
      OTM (Out of the Money):
        Call: stock price < strike price
        Put:  stock price > strike price

    Option Premium = Intrinsic Value + Extrinsic Value
      Intrinsic:  How much ITM the option is (never negative)
      Extrinsic:  Time value + implied volatility premium
                  Decays to zero at expiration (theta decay)

---

## The Greeks

    Delta (Δ):
      Measures price sensitivity to $1 move in underlying
      Call delta: 0 to +1   |   Put delta: -1 to 0
      ATM option: ~0.50 delta
      Deep ITM:   ~1.00 delta
      Deep OTM:   ~0.05 delta
      Use: hedge ratio, probability approximation (0.30 delta ~ 30% ITM at expiry)

    Gamma (Γ):
      Rate of change of delta per $1 move in underlying
      Highest for ATM options near expiration
      Long options: positive gamma (delta accelerates in your favor)
      Short options: negative gamma (delta accelerates against you)
      Gamma risk spikes in final week before expiry

    Theta (Θ):
      Time decay — how much premium erodes per day
      Always negative for long options (you lose value each day)
      Always positive for short options (you collect decay each day)
      Accelerates sharply in final 30 days
      ATM options decay fastest in absolute terms

    Vega (V):
      Sensitivity to 1% change in implied volatility
      Long options: positive vega (benefit from rising IV)
      Short options: negative vega (benefit from falling IV)
      Key insight: buy options before expected IV expansion (earnings)
                   sell options after IV spike to collect elevated premium

    Rho (ρ):
      Sensitivity to 1% change in interest rates
      More relevant for longer-dated options (LEAPS)
      Calls have positive rho, puts have negative rho

---

## Volatility

    Historical Volatility (HV):
      Actual realized volatility of the underlying over past N days
      Calculated from standard deviation of log returns

    Implied Volatility (IV):
      Market's expectation of future volatility
      Derived from option prices using Black-Scholes
      High IV = expensive options, Low IV = cheap options

    IV Rank (IVR):
      Where current IV sits vs past 52 weeks (0-100)
      IVR > 50 = elevated, good time to SELL options
      IVR < 30 = low, good time to BUY options

    IV Percentile (IVP):
      % of days in past year where IV was lower than current
      Similar to IVR but based on days count

    VIX:
      S&P 500 implied volatility index (fear gauge)
      VIX > 30 = high fear, elevated premiums
      VIX < 15 = complacency, cheap options

    Volatility Skew:
      Put options typically more expensive than calls (crash fear)
      Steep skew = market worried about downside
      Use: buy calls in high skew, sell puts when skew is extreme

---

## Options Strategies

### Bullish Strategies
    Long Call:
      Buy call at strike A
      Max profit: unlimited
      Max loss: premium paid
      Breakeven: strike A + premium
      Use: strong bullish with defined risk

    Cash-Secured Put (CSP):
      Sell put at strike A, hold cash to buy shares if assigned
      Max profit: premium collected
      Max loss: strike price - premium (shares go to zero)
      Breakeven: strike A - premium
      Use: want to buy stock at a discount, income generation

    Bull Call Spread:
      Buy call at strike A, sell call at strike B (B > A)
      Max profit: (B - A) - net debit
      Max loss: net debit paid
      Breakeven: strike A + net debit
      Use: bullish but want to reduce cost

    Covered Call:
      Own 100 shares + sell call at strike A
      Max profit: (strike A - stock cost) + premium
      Max loss: stock cost - premium (stock goes to zero)
      Use: income on existing shares, capped upside

### Bearish Strategies
    Long Put:
      Buy put at strike A
      Max profit: strike A - premium (stock to zero)
      Max loss: premium paid
      Breakeven: strike A - premium
      Use: strong bearish with defined risk, portfolio hedge

    Bear Put Spread:
      Buy put at strike A, sell put at strike B (B < A)
      Max profit: (A - B) - net debit
      Max loss: net debit
      Breakeven: strike A - net debit
      Use: bearish but reduce cost

### Neutral Strategies
    Iron Condor:
      Sell OTM put + buy further OTM put (bull put spread)
      Sell OTM call + buy further OTM call (bear call spread)
      Max profit: net credit received
      Max loss: width of wider spread - net credit
      Breakeven: short put strike - credit AND short call strike + credit
      Use: neutral, profit from time decay when price stays in range
      Best: high IVR environments (sell elevated premium)

    Iron Butterfly:
      Sell ATM call + sell ATM put (short straddle)
      Buy OTM call + buy OTM put (long strangle as wings)
      Higher credit than condor, narrower profit range
      Use: very neutral, stock pinned at strike at expiry

    Short Straddle:
      Sell ATM call + sell ATM put (same strike)
      Max profit: total premium collected
      Max loss: unlimited (undefined risk)
      Use: very neutral, high IV environment
      Risk: large move in either direction

    Short Strangle:
      Sell OTM put + sell OTM call (different strikes)
      More forgiving than straddle, lower premium
      Use: neutral with wide range, high IV

### Volatility Strategies
    Long Straddle:
      Buy ATM call + buy ATM put (same strike, expiry)
      Max profit: unlimited (big move either direction)
      Max loss: total premium paid
      Breakeven: strike +/- total premium
      Use: expecting big move, low IV environment, before earnings

    Long Strangle:
      Buy OTM call + buy OTM put
      Cheaper than straddle, needs bigger move to profit
      Use: expecting very large move, cheaper than straddle

---

## Black-Scholes Model
```python
import numpy as np
from scipy.stats import norm

def black_scholes(S, K, T, r, sigma, option_type='call'):
    """
    S: current stock price
    K: strike price
    T: time to expiry in years (e.g. 30 days = 30/365)
    r: risk-free rate (e.g. 0.05 for 5%)
    sigma: implied volatility (e.g. 0.20 for 20%)
    """
    d1 = (np.log(S/K) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
    d2 = d1 - sigma * np.sqrt(T)

    if option_type == 'call':
        price = S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)
    else:
        price = K * np.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)

    return round(price, 4)

def calculate_greeks(S, K, T, r, sigma, option_type='call'):
    d1 = (np.log(S/K) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
    d2 = d1 - sigma * np.sqrt(T)

    delta = norm.cdf(d1) if option_type == 'call' else norm.cdf(d1) - 1
    gamma = norm.pdf(d1) / (S * sigma * np.sqrt(T))
    theta_call = (-(S * norm.pdf(d1) * sigma) / (2 * np.sqrt(T))
                  - r * K * np.exp(-r * T) * norm.cdf(d2))
    theta = theta_call / 365 if option_type == 'call' else (
        theta_call + r * K * np.exp(-r * T)) / 365
    vega  = S * norm.pdf(d1) * np.sqrt(T) / 100
    rho   = (K * T * np.exp(-r * T) * norm.cdf(d2) / 100
             if option_type == 'call'
             else -K * T * np.exp(-r * T) * norm.cdf(-d2) / 100)

    return {
        'delta': round(delta, 4),
        'gamma': round(gamma, 4),
        'theta': round(theta, 4),
        'vega':  round(vega,  4),
        'rho':   round(rho,   4)
    }

def breakeven_prices(strike, premium, option_type='call'):
    if option_type == 'call':
        return {'upside_breakeven': strike + premium}
    else:
        return {'downside_breakeven': strike - premium}

def probability_of_profit(S, K, T, r, sigma, option_type='call'):
    d2 = ((np.log(S/K) + (r - 0.5 * sigma**2) * T)
          / (sigma * np.sqrt(T)))
    if option_type == 'call':
        return round(norm.cdf(-d2) * 100, 2)
    else:
        return round(norm.cdf(d2) * 100, 2)
```

---

## Systematic Options Selling Rules

    The 45 DTE Rule (tastytrade):
      - Sell options at ~45 days to expiration
      - Close at 50% of max profit (21 DTE)
      - Maximizes theta decay curve efficiency

    Position Sizing:
      - Never risk more than 5% of portfolio on single trade
      - Keep total delta exposure balanced (delta neutral)
      - Scale into positions, do not go full size at once

    High Probability Selling:
      - Sell at 30 delta or lower (70%+ probability OTM)
      - Higher probability = lower premium = more trades needed
      - Sweet spot: 16-30 delta for balance of premium vs safety

    The Wheel Strategy:
      Step 1: Sell CSP on stock you want to own at target price
      Step 2: If assigned, own shares at effective lower cost
      Step 3: Sell covered calls on shares at or above cost basis
      Step 4: If called away, back to Step 1
      Income machine on stocks you are long-term bullish on

---

## Common Pitfalls

| Pitfall | Problem | Fix |
|---|---|---|
| Ignoring IV rank | Selling cheap premium | Only sell when IVR > 50 |
| Too many contracts | One loss blows account | Max 5% risk per trade |
| Holding to expiry | Gamma risk explodes | Close at 50% profit or 21 DTE |
| Undefined risk in small account | One bad trade = margin call | Use spreads for defined risk |
| Buying options in high IV | Overpaying for premium | Buy options when IVR < 30 |
| Ignoring earnings risk | IV crush destroys long options | Check earnings dates always |
| Early assignment fear | Unnecessary panic | Only ITM options get assigned early |

---

## Best Practices

- **Know your max loss** before entering any trade
- **Sell in high IV, buy in low IV** — volatility mean reverts
- **Close winners early** — 50% of max profit is the target
- **Manage losers at 2x credit received** — cut at 200% loss
- **Diversify across underlyings** — never concentrate in one stock
- **Track P&L by strategy** — know what actually works for you
- **Paper trade new strategies** for at least 30 occurrences

---

## Related Skills

- **technical-analysis-expert**: Chart setups for options entries
- **finance-trading-expert**: Overall trading framework
- **risk-management-expert**: Portfolio-level options risk
- **quantitative-finance-expert**: Options pricing models deep dive