The Black Scholes Options Model is a simple mathematical formula used to value European options. A European option is an option to buy an asset (such as a share) on a single specified date; conversely, US 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, retracement options, or barrier options, as it cannot incorporate the more complex exercise characteristics of these options or their path dependencies such as entry / options. barrier exit. The main advantages of using Black Scholes is its speed and precision in titration.
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 has the right to buy or sell the underlying asset. This is usually a very simple entry, as it is specified in the option 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 After this date, the option is no longer valid.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 expiration of the option.
Volatility: This is probably the most important piece of information in the Black Scholes option pricing model. There are server methods for estimating volatility. Historical volatility uses historical prices for asset price movements to estimate volatility, while implied volatility uses implied volatility in the prices of traded options to estimate volatility.
Return (optional) – This is the average return generated by the asset over the period until the option expires. It can be a dividend (such as a stock or stock index) or, alternatively, the income generated by a commodity (for example, leasing fees paid for rented gold).
In general, it is difficult to forecast the return of the asset over the life of the option, so the historical performance of the asset is typically used.
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 a single volatility entry, and as such, derivatives specialists often use other option pricing models, such as lattice models or Monte Carlo simulations.