BS model is used to price european options . It is based on the ITO lemma and on some fundamentals hypothesis : The underlying price is a geometric brownian motion, volatility and free risk rates are known and fixed, no dividends, time is a continuous function, no arbitrage opportunity, no transaction costs, assets are infinitely divisible, shorting is permitted , no taxes , good liquidity, buying/selling cost spread is null . ( This list of assumptions is exhaustive )