greeks

Option pricing and Greeks under the Black-Scholes model.

Features

• Pricing — closed-form call and put prices
• Delta — first-order sensitivity to spot
• Gamma — second-order sensitivity to spot
• Vega — sensitivity to implied volatility
• Theta — time decay (per calendar day)
• Rho — sensitivity to the risk-free rate

Installation

This package is not published to PyPI — install it from the repository:

pip install git+https://github.com/Jebel-Quant/greeks.git

Or, to pin a release:

pip install git+https://github.com/Jebel-Quant/greeks.git@v0.1.1

Requires Python 3.11+.

Usage

from greeks import OptionType, price, delta, gamma, vega, theta, rho

S, K, T, r, sigma = 100.0, 100.0, 1.0, 0.05, 0.20

# Price
print(f"call  {price(S, K, T, r, sigma, OptionType.CALL):8.4f}")
print(f"put   {price(S, K, T, r, sigma, OptionType.PUT):8.4f}")

# Greeks
print(f"delta {delta(S, K, T, r, sigma, OptionType.CALL):8.4f}")
print(f"gamma {gamma(S, K, T, r, sigma):8.4f}")
print(f"vega  {vega(S, K, T, r, sigma):8.4f}")
print(f"theta {theta(S, K, T, r, sigma, OptionType.CALL):8.4f}")  # per day
print(f"rho   {rho(S, K, T, r, sigma, OptionType.CALL):8.4f}")

call   10.4506
put     5.5735
delta   0.6368
gamma   0.0188
vega   37.5240
theta  -0.0176
rho    53.2325

Those numbers are executed and diffed against this block on every CI run, so they cannot go stale silently.

API reference

Every function takes the market parameters (S, K, T, r, sigma); price, delta, theta, and rho also take an optional option_type (defaults to OptionType.CALL). All return a float.

Function	Signature	Returns
price	price(S, K, T, r, sigma, option_type=CALL)	Option price
delta	delta(S, K, T, r, sigma, option_type=CALL)	∂Price/∂S — sensitivity to spot
gamma	gamma(S, K, T, r, sigma)	∂²Price/∂S² — same for calls and puts
vega	vega(S, K, T, r, sigma)	∂Price/∂sigma — same for calls and puts
theta	theta(S, K, T, r, sigma, option_type=CALL)	∂Price/∂t — per calendar day
rho	rho(S, K, T, r, sigma, option_type=CALL)	∂Price/∂r — sensitivity to the rate

OptionType is a StrEnum with members OptionType.CALL ("call") and OptionType.PUT ("put").

Parameter conventions

Symbol	Description
S	Spot price
K	Strike price
T	Time to expiry in years
r	Continuously compounded risk-free rate (e.g. 0.05 for 5%)
sigma	Annualised volatility (e.g. 0.20 for 20%)

• Vega is per 1-point move in sigma (i.e. per 100 vol-points), not per percentage point.
• Rho is per 1-point move in r, not per basis point.
• Theta is per calendar day.

Input validation

S, K, T, and sigma must be finite and strictly positive; r must be finite (it may be negative). Any other value raises ValueError rather than returning a NaN/inf result, so degenerate inputs fail loudly at the call site.

Stability

This project follows semantic versioning. While the version is 0.x, the public API (the functions and OptionType exported from greeks) may change in a backwards-incompatible way in any minor release; breaking changes will be called out in the release notes. From 1.0.0 onward, breaking changes to the public API will only ship in a major release.

Development

make install   # create virtualenv and install dependencies
make test      # run test suite
make fmt       # lint and format
make all       # full quality gate