Black Scholes Model
The Black-Scholes model is a mathematical model used to calculate the theoretical price of a European call or put option, named after its creators Fischer Black and Myron Scholes. The model was introduced in 1973 and has since become one of the most widely used models in finance.
The Black-Scholes model assumes that the underlying asset price follows a log-normal distribution and that there are no arbitrage opportunities in the market. It also assumes that the option can be exercised only at expiration, that the option is European (i.e., it cannot be exercised before expiration), and that there are no transaction costs.
The model uses several inputs to calculate the theoretical price of an option, including the current stock price, the strike price of the option, the time until expiration, the risk-free interest rate, and the volatility of the stock price.
The Black-Scholes model has several important implications for investors. First, it suggests that the value of an option is influenced by several factors, including the underlying asset price, the strike price, the time until expiration, the risk-free interest rate, and the volatility of the stock price.
Second, the Black-Scholes model suggests that options can be used to manage risk and create trading opportunities. For example, investors can use options to protect their portfolios from downside risk or to speculate on the future direction of the market.
Despite its widespread use, the Black-Scholes model has been criticized for its assumptions and limitations. For example, the model assumes that the stock price follows a log-normal distribution, which may not always be true in practice. Additionally, the model assumes that there are no transaction costs, which may not be the case in the real world.
In conclusion, the Black-Scholes model is a widely used mathematical model for calculating the theoretical price of a European call or put option. While the model has its limitations, it remains an important tool for managing risk and creating trading opportunities in the financial markets.