Introduction to the Black Scholes Options Pricing Model
The Black Scholes Option Model is a simple mathematical formula used to price European options. A European option is an option to buy an asset (such as a share) on a single specified date; In contrast, American options allow the holder the right to buy at any time up to the option’s expiration date.
The Black Scholes model is not suitable for valuing other types of options, such as American options, backwards options, or barrier options, as 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 valuation accuracy.
Black Scholes has five main inputs: spot price, strike price, time to maturity, 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 is entitled to buy or sell the underlying asset. This is usually a very simple input, as it is specified in the option’s documentation.
Time to Expiration: The time (in years) until the option expires. After this date, the option is no longer valid.
Interest Rate: The risk-free interest rate for the term to maturity 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 implied volatility of traded option prices to estimate volatility.
Yield (optional) – This is the average return generated by the asset over the period until the option expires. This can be a dividend (such as a stock or stock index) or alternatively the income generated by a commodity (for example, leasing fees paid on rented gold).
It is generally difficult to forecast the return of the asset over the life of the option, so the historical return of the asset is typically used instead.
However, Black Scholes has several limitations in addition to the limited types of options they can price. 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.
