crypto-bs 0.5.0

Python library for pricing coin-settled crypto options

Crypto Black-Scholes

Version 0.5.0 — Python library for pricing coin-settled cryptocurrency options with Black-76 and Black-Scholes-style models, Greeks, portfolio aggregation, Deribit-oriented helpers, historical volatility estimators, GEX/vol-regime analytics, and an implied-volatility surface foundation.

See CHANGELOG.md for release notes and breaking changes.

Features

• Pricing — Black-76 (forward / coin premium), enhanced Black-Scholes with USD vs coin-denominated premium
• Greeks — Delta (USD vs coin premium), gamma, theta, vega, rho; second-order Greeks (speed, charm, vanna, vomma) via finite differences in GreeksCalculator
• Portfolio — Multi-position Greeks, risk metrics, gamma exposure profile
• Data — Deribit REST helpers (timeouts on HTTP calls)
• IV — Implied vol from market price (Brent’s method), intrinsic and bounds checks
• Vectorized chain pricing — price_options_vectorized for many strikes / expiries at once
• Breakeven — USD and coin-settled breakeven helpers
• Historical volatility — Close-to-close, Parkinson, Rogers-Satchell, Yang-Zhang estimators
• GEX analytics — Net gamma exposure by strike, cumulative GEX, gamma flip point
• Volatility regimes — Term-structure and skew regime classifier with simple signal synthesis
• Volatility surface foundation — Fit/interpolate IV over strike and maturity

Model overview

1. Black-76 (module-level price_option) — Forward F, undiscounted coin premium; suited to Deribit-style quoting.
2. BlackScholesModel — Spot-based Merton BS; is_coin_based=True for premium as fraction of spot; exposes delta_usd (hedge delta) and delta_coin (premium sensitivity to spot).
3. Portfolio — Aggregations use USD delta per position for total_delta and dollar exposures.

Installation

pip install -U crypto-bs

Import as:

import crypto_bs

Requires Python ≥3.10, numpy, scipy, pandas, requests (see pyproject.toml).

Upgrading from 0.1.x

• Replace result.delta with result.delta_usd (hedging / notional delta) and/or result.delta_coin (academic / premium-in-coin sensitivity).
• Dicts from price_coin_based_option / validate_deribit_pricing: use delta_usd / delta_coin instead of delta.
• get_btc_volatility() remains unimplemented in data_fetch; use crypto_bs.historical_vol functions for realized volatility from OHLC data.
• Optional: add pytest to your environment for the test suite (pip install pytest).

Quick start

from crypto_bs import price_option, delta, gamma, price_options_vectorized
import numpy as np

# Black-76 coin premium
price = price_option(F=110000, K=105000, T=1/365, sigma=0.6, option_type='call')
print(f"Premium (coin): {price:.6f}")

d = delta(110000, 105000, 1/365, 0.6, 'call')
g = gamma(110000, 105000, 1/365, 0.6)

# Whole chain in one call
K = np.array([100000.0, 105000.0, 110000.0])
T = np.full(3, 1 / 365)
sig = np.full(3, 0.6)
types = np.array(["call", "call", "put"])
premiums = price_options_vectorized(110000, K, T, sig, types)

Breakeven

from crypto_bs import breakeven_price, breakeven_price_coin_based

be_usd = breakeven_price(105000, 500, 'call')
be_coin = breakeven_price_coin_based(105000, price, 'call')

Advanced usage

Coin-based BlackScholesModel

from crypto_bs import BlackScholesModel, OptionParameters, OptionType

bs_model = BlackScholesModel()
params = OptionParameters(
    spot_price=110000,
    strike_price=105000,
    time_to_maturity=1/365,
    volatility=0.6,
    option_type=OptionType.CALL,
    is_coin_based=True,
)

result = bs_model.calculate_option_price(params)
print(f"Coin premium: {result.coin_based_price:.6f}")
print(f"USD equivalent: ${result.usd_price:.2f}")
print(f"Delta USD (hedge): {result.delta_usd:.6f}")
print(f"Delta coin premium: {result.delta_coin:.9f}")

Portfolio risk

from crypto_bs import analyze_portfolio_risk

portfolio = [
    {
        "quantity": 10,
        "spot_price": 110000,
        "strike_price": 105000,
        "time_to_maturity": 1/365,
        "volatility": 0.6,
        "option_type": "call",
        "underlying": "BTC",
        "is_coin_based": True,
    }
]

risk = analyze_portfolio_risk(portfolio)
print("Portfolio delta (USD):", risk["portfolio_summary"]["total_delta"])
print("Gamma exposure:", risk["risk_metrics"]["gamma_exposure"])

Deribit helpers

from crypto_bs import get_btc_forward_price, get_option_data, validate_deribit_pricing

F = get_btc_forward_price()
option_data = get_option_data("BTC-3SEP25-105000-C")

validation = validate_deribit_pricing(
    deribit_price_btc=option_data["mark_price"],
    spot=F,
    strike=105000,
    time_to_maturity=1/365,
    option_type="call",
)
print("IV:", validation["implied_volatility"])
print("Delta USD:", validation["delta_usd"])

Requests use a 10-second timeout; failures surface as requests exceptions or ValueError from the API helpers.

Historical volatility

import pandas as pd
from crypto_bs import close_to_close_hv, parkinson_hv, yang_zhang_hv

# Example OHLC arrays as pandas Series
close = pd.Series([100, 102, 101, 104, 103, 106, 108])
high = close * 1.01
low = close * 0.99
open_ = close.shift(1).fillna(close.iloc[0])

hv_cc = close_to_close_hv(close, window=5)
hv_parkinson = parkinson_hv(high, low, window=5)
hv_yz = yang_zhang_hv(open_, high, low, close, window=5)

GEX and volatility analytics

import pandas as pd
from crypto_bs import compute_gex, gex_summary, VolatilityAnalytics

chain = pd.DataFrame({
    "strike": [90000, 100000, 110000, 90000, 100000, 110000],
    "time_to_maturity": [30/365] * 6,
    "volatility": [0.7] * 6,
    "option_type": ["call", "call", "call", "put", "put", "put"],
    "open_interest": [1200, 1800, 900, 1400, 2000, 1300],
})
gex_df = compute_gex(chain, spot=100000)
print(gex_summary(gex_df, spot=100000))

term = pd.Series([0.85, 0.72, 0.65], index=[7/365, 30/365, 90/365])
skew = pd.Series([0.04, 0.035, 0.03], index=[7/365, 30/365, 90/365])
va = VolatilityAnalytics(atm_term_structure=term, skew_by_maturity=skew)
print(va.ts_regime(), va.skew_regime(), va.trading_signal())

Volatility surface

import pandas as pd
from crypto_bs import VolatilitySurface

chain = pd.DataFrame({
    "strike": [90000, 100000, 110000, 90000, 100000, 110000],
    "time_to_maturity": [30/365, 30/365, 30/365, 90/365, 90/365, 90/365],
    "implied_volatility": [0.74, 0.70, 0.73, 0.66, 0.62, 0.65],
})
surface = VolatilitySurface()
surface.fit(chain)
print(surface.get_iv(105000, 60/365))
print(surface.get_term_structure())

API reference (summary)

Symbol	Role
price_option, black_76_call, black_76_put	Scalar Black-76 coin premium
price_options_vectorized	Vectorized chain pricing
delta, gamma, vega, theta, rho	Black-76 Greeks on forward F; rho(..., risk_free_rate=0)
breakeven_price, breakeven_price_coin_based	Breakeven spot levels
BlackScholesModel, OptionParameters, OptionPricing	Full pricing + Greeks; OptionPricing.delta_usd / delta_coin
calculate_implied_volatility	IV search; default max vol 20.0; validates vs intrinsic
GreeksCalculator, calculate_option_greeks, analyze_portfolio_risk	Profiles and portfolio
get_btc_forward_price, get_option_data, get_available_instruments, get_btc_price	Market data
get_btc_volatility	Not implemented — raises NotImplementedError
close_to_close_hv, parkinson_hv, rogers_satchell_hv, yang_zhang_hv, vol_premium	Historical volatility analytics
compute_gex, find_gamma_flip, gex_summary	Gamma exposure analytics
VolatilityAnalytics	Term structure/skew regimes and trading signal
VolatilitySurface	IV surface fit/interpolation and sanity checks

Full signatures and defaults are in the source docstrings.

Validation (example)

Using real Deribit-style numbers, model vs mark can be on the order of ~1% in BTC premium depending on mark, forward, and IV; use validate_deribit_pricing and live get_option_data for your own checks.

Testing

# From repo root (recommended)
pytest tests/ -v

# With conda
conda activate crypto-option
cd /path/to/crypto_bs_project
PYTHONPATH=. pytest tests/ -v

# Wrapper script
python run_tests.py

The suite includes 36 tests (pricing, Greeks, IV, historical vol, GEX, regime analytics, surface interpolation, and parity/data checks). Install pytest if it is not already in the environment.

License and links

• License: see LICENSE in the repository.
• Repository: github.com/MhmdFasihi/crypto_black_scholes
• Changes / migration: CHANGELOG.md

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Built for cryptocurrency options workflows that need coin-settled premiums, explicit hedge delta vs coin-premium delta, and portfolio Greeks.