Black-Scholes Option Valuation and Periodic Delta Hedging

Summary

This indicator and strategy script estimates European call and put values with Black-Scholes formulas, using a normal cumulative distribution approximation. Inputs cover option type, strike, expiry, the underlying price source, risk-free rate source, and volatility mode. The script also exposes a broad set of option metrics, including Greeks and probability of touch, for chart display. Volatility can come from an implied-volatility symbol, a realized-volatility calculation, or a custom input; the risk-free input can use a market symbol or a crypto funding-rate series.

The trading component offers simple and synthetic hedging modes, with position size and hedge interval settings, and closes the hedge after expiry. The source is an implementation example rather than validation of model accuracy or hedge performance. Its estimates depend on data-source choices and model assumptions, and the displayed code does not establish that its inputs or hedge rules are suitable for every option style; despite selectable styles, the shown pricing formulas are vanilla call and put formulas.

Key ideas

• The script calculates theoretical vanilla call and put prices using Black-Scholes inputs.
• Volatility may be supplied as implied, estimated from realized price movement, or entered manually.
• The interface can display option sensitivities and other derived measures.
• Simple and synthetic modes adjust an underlying position as a hedge at configured intervals.
• The code offers no empirical evidence that its prices or hedging approach perform reliably in live markets.

Tags

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