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

pip install greeks

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
call_price = price(S, K, T, r, sigma, OptionType.CALL)   # ~10.45
put_price  = price(S, K, T, r, sigma, OptionType.PUT)    # ~5.57

# Greeks
d = delta(S, K, T, r, sigma, OptionType.CALL)   # ~0.637
g = gamma(S, K, T, r, sigma)                    # ~0.019
v = vega(S, K, T, r, sigma)                     # ~37.52
t = theta(S, K, T, r, sigma, OptionType.CALL)   # ~-0.018  (per day)
p = rho(S, K, T, r, sigma, OptionType.CALL)     # ~53.23

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.

Development

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