Black Scholes Option Pricing Model

This model can only be used for valuing European Options as it cannot handle the early exercise feature of American Options (which should be valued using a binomial model). The primary advantages are its speed and accuracy.

Inputs to Black Scholes Option Model

Spot Price :
The market price of the underlying asset on the valuation date. This can be a difficult input to estimate for options on illiquid assets, however under normal circumstances the closing market price can usually be used

Strike Price :
This is the price level at which the option holder has the right to buy or sell the underlying asset. It is the most straightforward input as it will always be given in the option contract.

Time to Maturity :
The time (in years) until the option expires and the holder is no longer entitled to exercise the option.

Interest Rate :
The risk free interest rate for the period until the option expires. The risk free rate should typically be a zero coupon government bond yield.

Volatility :
Volatility is probably the most important single input to any option pricing model. There are numerous methods for estimating volatility.
Historic volatility entails using historic price data for share price movements. A key issue is how far into the past to collect data from. A useful rule of thumb is to collect data from as far back as the options term (eg a option with a 5 year life would require an input of historic volatility calculated from the last 5 years of historic data).
Historic volatility is often considered as flawed as it assumes the past will reflect the future - thus several forward-looking measures of volatility can be more powerful and accurate:
Implied Volatility is the volatility implied by the market price of traded options. As the price is already known and the volatility (which is typically an input) is unknown the pricing model is reversed to determine the volatility. When using the implied volatility it is important to be aware of the volatility surface. The volatility surface is the 3 dimensional representation of the relationship between volatility, option life and exercise price. Thus to use implied volatility the option from which the volatility is implied should have a similar life and exercise price (or ratio of market price to exercise price) as the option being valued.
Other models such as ARCH, EWMA, GARCH use historic data and condition the data using factors such as mean reversion to acheive a more accurate volatility forecast.

Yield :
The average yield generated by the underlying asset for the life of the option. This can be either a dividend (for a stock or stock index) or the income generated by a commodity.
It is often difficult to forecast the yield for the entire option life so the current yield of the asset is often used.

DerivativeOne features a free black scholes pricing model for valuing European options on Stocks, Currencies, Commodities and Futures