The Black Scholes option model is a simple mathematical formula used to value European options. A European option is an option to buy an asset (such as a stock) on a single specified date; By contrast, American options allow the holder the right to buy at any time up to the expiration date of the option.
The Black Scholes model is not suitable for pricing other types of options, such as American options, back options, or barrier options, since it cannot incorporate the more complex exercise characteristics of these options or their path dependencies, such as barrier entry/exit options. The main advantages of using Black Scholes is its speed and accuracy of titration.
Black Scholes has five main inputs: spot price, strike price, time to expiration, interest rate, and volatility.
Spot Price: The open market price of the underlying asset on the valuation date, such as the closing price of a share on a stock exchange.
Strike Price: The price at which the option holder has the right to buy or sell the underlying asset. This is usually a very simple entry, as it is specified in the option’s documentation.
Time to Expiration: The time (in years) until the expiration of the option. After this date, the option is no longer valid.
Interest Rate: The risk-free interest rate for the term to expiration of the option.
Volatility – This is probably the most important input to the Black Scholes option pricing model. There are server methods to estimate volatility. Historical volatility uses the historical prices of asset price movements to estimate volatility, while implied volatility uses the volatility implied in the prices of traded options to estimate volatility.
Yield (optional): This is the average return generated by the asset during the period until the expiration of the option. This can be a dividend (such as a stock or stock index) or, alternatively, income generated from a commodity (for example, lease fees paid on rented gold).
It is generally difficult to forecast the return on the asset over the life of the option, so the historical return on the asset is often used instead.
However, Black Scholes has several limitations in addition to the limited types of options that they can value. It can only accommodate a single interest rate and volatility input, and as such, derivatives specialists often use other option pricing models, such as lattice models or Monte-Carlo simulations.
