Options trading

Skill: Options Trading | Domain: trading | Category: asset-class | Level: advanced Tags: trading, asset-class, options, greeks, iv, multi-leg, volatility

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Options Trading Skill

Overview

Complete options pricing and strategy analysis toolkit. Implements Black-Scholes (1973) pricing, all five first-order Greeks plus second-order (charm, vanna, volga), implied volatility extraction, multi-leg strategy payoff analysis, IV surface construction, and option chain screening.

Python Module

xtrading/skills/options.py

Stack

• scipy.stats.norm — Black-Scholes d1/d2 cumulative normal
• scipy.optimize.brentq — Implied volatility root finding
• numpy — Vectorised payoff calculations and Monte Carlo
• pandas — Option chain and surface management

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1. Options Pricing — Black-Scholes

from xtrading.skills.options import OptionsPricing

# European call price
price = OptionsPricing.black_scholes(S=100, K=100, T=0.25, r=0.05, sigma=0.20, option_type="call")
# → ~5.07

# Put-call parity holds:
# call - put = S - K * exp(-rT)

# Implied volatility (Brent solver)
iv = OptionsPricing.implied_volatility(
    market_price=5.0, S=100, K=100, T=0.25, r=0.05, option_type="call"
)
# → 0.1963 (≈20% IV)

# Binomial tree (American options)
am_put = OptionsPricing.binomial_price(
    S=100, K=100, T=0.25, r=0.05, sigma=0.20, option_type="put", american=True
)

# Monte Carlo with confidence interval
mc = OptionsPricing.monte_carlo_price(S=100, K=100, T=0.25, r=0.05, sigma=0.20, n_paths=100_000)
# → {"price": 5.07, "std_error": 0.02, "ci_95_lower": 5.03, "ci_95_upper": 5.11}

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2. Greeks Calculator

from xtrading.skills.options import GreeksCalculator

# All Greeks in one call
greeks = GreeksCalculator.all_greeks(S=100, K=100, T=0.25, r=0.05, sigma=0.20, option_type="call")
# {
#   "price": 5.07, "delta": 0.5377, "gamma": 0.0394,
#   "theta": -0.0451, "vega": 0.1974, "rho": 0.1220,
#   "charm": -0.00015, "vanna": 0.0789, "volga": 0.3948,
#   "moneyness": "ATM", "intrinsic": 0.0, "time_value": 5.07
# }

# Individual Greeks
delta = GreeksCalculator.delta(S=105, K=100, T=0.25, r=0.05, sigma=0.20, option_type="call")
# → 0.726 (ITM call, delta > 0.5)

gamma = GreeksCalculator.gamma(S=100, K=100, T=0.25, r=0.05, sigma=0.20)
# → 0.0394 (always positive)

theta = GreeksCalculator.theta(S=100, K=100, T=0.25, r=0.05, sigma=0.20, option_type="call")
# → -0.0451 per day (time decay)

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3. Strategy Builder — Multi-Leg Analysis

from xtrading.skills.options import StrategyBuilder

# Bull Call Spread
builder = StrategyBuilder.bull_call_spread(
    symbol="SPY", S=100, K_long=100, K_short=110,
    T=0.25, r=0.05, sigma=0.20
)
result = builder.analyse()
# result.strategy_name = "Bull Call Spread"
# result.net_premium   = -1.23  (debit: negative)
# result.max_profit    = 8.77
# result.max_loss      = -1.23
# result.breakeven_prices = [101.23]
# result.risk_reward   = 7.13
# result.probability_of_profit = 0.41

# Iron Condor
ic = StrategyBuilder.iron_condor(
    symbol="SPX", S=4000,
    K_put_long=3800, K_put_short=3900,
    K_call_short=4100, K_call_long=4200,
    T=0.25, r=0.05, sigma=0.18
)
result = ic.analyse()
# result.net_premium = +3.45  (credit)
# result.max_profit  = 3.45
# result.max_loss    = -96.55

# Long Straddle
straddle = StrategyBuilder.long_straddle(
    symbol="AAPL", S=150, K=150, T=0.25, r=0.05, sigma=0.35
)
result = straddle.analyse()
# Two breakeven prices: [139.xx, 160.xx]

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4. Volatility Surface

import pandas as pd
from xtrading.skills.options import VolatilitySurface

# Build from option chain data
surface_data = pd.DataFrame({
    "strike": [90, 95, 100, 105, 110, 90, 95, 100, 105, 110],
    "expiry_days": [30]*5 + [60]*5,
    "iv": [0.25, 0.22, 0.20, 0.21, 0.23, 0.27, 0.24, 0.22, 0.23, 0.25],
})
vs = VolatilitySurface(surface_data)

# Smile at 30-day expiry
smile = vs.smile_at_expiry(expiry_days=30, atm_strike=100)
# {"atm_iv": 0.20, "skew_25d": -0.02, "butterfly_25d": 0.015, "bias": "put_skew"}

# Term structure
ts = vs.term_structure(atm_strike=100)
# DataFrame: expiry_days → atm_iv, vix_equiv, annualised_cost_pct

# IV Rank
import numpy as np
hist = pd.Series(np.linspace(0.10, 0.40, 252))
rank = vs.iv_rank(current_iv=0.30, historical_ivs=hist)
# {"iv_rank": 66.7, "regime": "NORMAL_IV", "strategy_bias": "NEUTRAL"}

# Arbitrage check
arb = vs.validate_no_arbitrage()
# {"arbitrage_free": True, "violations": [], "n_violations": 0}

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5. Option Screener

from xtrading.skills.options import OptionScreener

screener = OptionScreener(chain_df, underlying_price=100.0, r=0.05)

# Screen for short-premium setups (30-60 DTE, 0.20-0.45 delta)
candidates = screener.screen(
    min_pop=0.60, min_dte=30, max_dte=60,
    min_delta=0.20, max_delta=0.45,
    option_type="put",
)

# Expected move calculation
em = screener.expected_move(expiry_days=30)
# {"expected_move_pts": 5.07, "expected_move_pct": 5.07,
#  "upper_bound": 105.07, "lower_bound": 94.93}

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Usage Conventions

1. All prices — same currency units as S and K
2. T — always in years (30 days = 30/365 = 0.082)
3. sigma — annualised decimal (20% = 0.20)
4. r — annualised risk-free rate decimal
5. Theta — returned as per-day (divide annual by 365 internally)
6. Vega — returned per 1% IV move (divide annual by 100 internally)
7. Put-call parity — always verified for European options

Key Formulas

Black-Scholes Call: S*N(d1) - K*exp(-rT)*N(d2)
Black-Scholes Put:  K*exp(-rT)*N(-d2) - S*N(-d1)
d1 = [ln(S/K) + (r + σ²/2)*T] / (σ*√T)
d2 = d1 - σ*√T

Delta (call) = N(d1)
Delta (put)  = N(d1) - 1
Gamma        = N'(d1) / (S*σ*√T)
Theta (call) = [-S*N'(d1)*σ/(2√T) - r*K*exp(-rT)*N(d2)] / 365
Vega         = S*√T*N'(d1) / 100

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Related Skills

• Technical Analysis
• Risk And Portfolio
• Statistical Analysis
• Portfolio Optimization