Pro Tier Module
Black-Scholes Options Pricer with Greeks
Black-Scholes-Merton pricing and the full Greek set, with an honest conditioning verdict on every number.
This tool runs inside GDBS Pro. What it computes and the authorities it applies are below.
The problem
Desk and risk teams need a trustworthy European option price and Greeks, but most calculators give a bare number with no signal of when deep ITM or near-expiry cancellation has eroded its digits.
The local-first solution
This plugin evaluates the exact Black-Scholes-Merton closed form and analytic Greeks in pure in-browser f64, using a Cody-class cumulative-normal and probing the cancelling difference with the GeoNum kernel to attach an honest trust verdict. Your rate, yield, volatility, and valuation date are echoed back and nothing is uploaded.
What it does
European call and put prices via the exact Black-Scholes-Merton closed form with continuous dividend yield
First-order Greeks: delta, gamma, theta, vega, and rho
Vega and rho per unit and per percentage point; theta per year and per calendar day
Put-call parity check to f64 precision
Cody/Hart-class cumulative-normal accurate to roughly machine precision
GeoNum conditioning verdict (PRECISE to UNRELIABLE) on the cancelling price difference
Honest scope
The BSM closed form, analytic Greeks, and parity hold to f64 precision; r, q, and sigma are dated market inputs you confirm for your valuation date, with the default rate seeded from a cited Treasury level you must verify. American early exercise, discrete dividends, the volatility smile, stochastic rates or vol, and second-order Greeks beyond gamma are not modeled - a model price is not a market price, and this is not investment or trading advice.
Authorities cited
- Black, F. & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy 81(3), 637-654. DOI 10.1086/260062. (The call/put closed form.)
- Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics and Management Science 4(1), 141-183. DOI 10.2307/3003143. (Continuous dividend yield q extension; put-call parity.)
- Hull, J. C. (2017). Options, Futures, and Other Derivatives, 10th ed., Ch.15 & 19, Pearson. (The Greek formulas: delta, gamma, theta, vega, rho - including the e^{-qT} dividend-adjusted forms.)
- Cody, W. J. (1969). Rational Chebyshev Approximation for the Error Function. Mathematics of Computation 23(107), 631-637. DOI 10.2307/2004390. (The erf/erfc rational minimax used here for N(x); abs error < ~1.2e-16; the netlib SPECFUN/CALERF algorithm.)
- Hart, J. F. et al. (1968). Computer Approximations. Wiley/SIAM. (Companion rational-approximation reference for the elementary-function evaluation regime split.)
- U.S. Treasury - Daily Treasury Par Yield Curve Rates / FRED series DGS1 (1-year constant-maturity yield). The default risk-free rate r is a dated as-of figure (~4.2% as of 2026-06-22) you confirm for your valuation date and tenor.
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Price an option now
Run the pricer in the browser and route results into a Sandbox workspace, a Worklog case, or a Gate client portal. Nothing is uploaded to anyone's cloud.