Black–Scholes Option Prices and Greeks with Historical Volatility Choices

Summary

This charting tool calculates theoretical call and put values using the Black–Scholes framework and displays their sensitivities. Its functions cover first-, second-, and third-order Greeks, including delta, gamma, vega, theta, rho, vanna, vomma, and other measures. The normal cumulative distribution used in pricing is approximated numerically, and the script includes several historical volatility estimators based on close-to-close, high-low, and open-close data, plus an exponentially weighted approach.

The indicator is restricted to daily charts and exposes model inputs for option terms and market assumptions. Its output is a model estimate, not a quoted market price or a guarantee of executable value; the document supplies no performance study or empirical validation. Results depend on the assumptions and volatility estimator selected, and users should check the implementation and inputs before relying on displayed prices or sensitivities. The source also contains many calculations but gives little explanatory discussion of when each estimator or Greek is most useful.

Key ideas

• The tool computes theoretical call and put prices using Black–Scholes assumptions.
• It calculates a broad set of first-, second-, and third-order option sensitivities.
• Several historical volatility estimators are provided, including range-based and close-based methods.
• The normal cumulative distribution is evaluated with numerical integration.
• The indicator requires daily chart data, and the document provides no empirical validation of its estimates.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.