Black–Scholes Pricing and Greeks for Vanilla, Binary, and Geometric Asian Options

Summary

This indicator estimates option values and sensitivities from spot, strike, time to expiry, an interest rate proxy, and volatility. It implements Black–Scholes call and put pricing for European vanilla options and offers additional calculations for binary options and geometric-average Asian options. Users can select an option side and choose a Greek to display, including delta, gamma, theta, vega, rho, and higher-order sensitivities. It also estimates probability of touch from delta.

Volatility can come from user input or an estimate based on recent log returns; the risk-free rate is selected through a currency-linked government bond yield series. The document includes formulas and configurable inputs, but reports no pricing comparison or empirical validation. Model assumptions, the quality and availability of rate and volatility inputs, and the specialized approximations for binary and Asian contracts limit how literally the outputs should be interpreted. It is a chart-based implementation of theoretical estimates, not evidence that a quoted market price is fair.

Key ideas

• The script calculates European call and put values using the Black–Scholes framework.
• It supports binary and geometric-average Asian option styles in addition to vanilla options.
• Users can display several first-, second-, and third-order Greeks, along with a delta-based touch estimate.
• Volatility may be supplied by the user or estimated from recent returns, while rates are mapped to bond-yield series.
• The document gives implementation formulas but no validation against traded option prices.

Tags

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