# Black-Scholes

The Black-Scholes model, aka the Black-Scholes-Merton (BSM) model, is a differential equation widely used to price options contracts. The indicator is developed in 1973 by Fischer Black, Robert Merton, and Myron Scholes.

## Description

The indicator's values are displayed in the chart Status Line. This mathematical equation estimates the theoretical value of derivatives other investment instruments, taking into account the impact of time and other risk factors.

Black-Scholes posits that instruments, such as stock shares or futures contracts, will have a lognormal distribution of prices following a random walk with constant drift and volatility. Using this assumption and factoring in other important variables, the equation derives the price of a European-style call option. The Black-Scholes model requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.

The Black-Scholes indicator is based on the Black Scholes option pricing model calculation. It plots the theoretical value of an option based on the underlying symbol in the chart.

When applied to a chart, this indicator displays one plot in a separate subchart from the main data series.

## Default Inputs

**ExpMonth_MM( 0 )** sets the month (1-12) the option expires.

**ExpYear_YYYY( 0 )** sets the year the option expires.

**StrikePr( 0 )** sets the option strike price.

**Rate100( 0 )** sets the risk free interest rate.

**Volty100( 0 )** sets the annualized volatility value.

**PutCall( put )** sets the option type.