Option Greeks

Server-computed Greeks

The option/*/greeks/* reference endpoints return Greeks computed by ThetaData using the Black-Scholes model — specifically the formulas catalogued on Wikipedia's Greeks page. Input conventions:

• Risk-free rate defaults to SOFR; override the source with rate_type (SOFR or a Treasury tenor) or pin an exact rate with rate_value.
• Dividends are ignored unless you pass annual_dividend.
• Option price input is the NBBO midpoint by default; use_market_value switches snapshot calculations to the market value, and trade-Greeks endpoints use the trade price.
• Underlying price input is the last underlying trade; underlyer_use_nbbo switches to the underlying NBBO midpoint.
• Implied volatility is solved numerically from the option price; each row carries an iv_error residual so you can judge the fit.
• version selects the calculation revision; latest uses real time-to-expiration down to a one-hour floor.

Local calculator

The SDK also ships an offline Black-Scholes calculator — all_greeks(...) and implied_volatility(...) in every language — that computes the value, first- through third-order Greeks (delta, gamma, theta, vega, rho, vanna, charm, vomma, veta, speed, zomma, color, ultima, epsilon, lambda, vera, dual delta, dual gamma, d1, d2), and IV via bisection, with no server round trip and no subscription.

from thetadatadx import all_greeks

g = all_greeks(spot=450.0, strike=455.0, rate=0.05, div_yield=0.015,
               tte=30 / 365, option_price=8.50, right="C")
print(g.iv, g.delta, g.gamma)

Inputs are spot, strike, rate, dividend yield (both as decimals: 0.05 = 5%), time to expiration in years, the market option price, and the right. The same seven arguments drive the iv / greeks CLI subcommands and the MCP server's offline tools.

Greek-by-Greek field definitions appear on every Greeks reference page's response table.