The BSM model is based on the following assumptions:
The market is completely efficient, that is, there is no arbitrage opportunity;
The change of stock price conforms to the model of geometric Brownian motion, that is, the change of stock price obeys normal distribution, and the standard deviation of this distribution is constant;
Stock price does not pay dividends;
The risk-free interest rate is known and constant.
According to the above assumptions, BSM model can calculate the theoretical price of European options, that is, the value of options on the expiration date (exercise date). This price is determined by five factors: stock price, exercise price, risk-free interest rate, option expiration time and stock volatility.
BSM model is widely used in European option pricing in stock, index, futures and other financial markets. Its advantages are simple and easy to use, high calculation efficiency and intuitive derivation process, so it can accurately predict the price change of options. However, BSM model also has some shortcomings, such as inapplicability to the pricing of American options and some errors in forecasting the volatility of stock prices.