mahmoud20138 Skill: Options Trading | Domain: trading | Category: asset-class | Level: advanced Tags:
trading,asset-class,options,greeks,iv,multi-leg,volatility
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
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}
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)
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]
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}
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}
Usage Conventions
- All prices — same currency units as S and K
- T — always in years (30 days = 30/365 = 0.082)
- sigma — annualised decimal (20% = 0.20)
- r — annualised risk-free rate decimal
- Theta — returned as per-day (divide annual by 365 internally)
- Vega — returned per 1% IV move (divide annual by 100 internally)
- 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