The Risk of Black-Scholes Option Pricing

The Black-Scholes option pricing formula is derived with the assumption that the hedging is continuous. In practice, there is no trading when the stock market is closed. So the adjustment of portfolios is discontinuous, and the risk of option pricing exists. We consider the risk of option pricing caused by this kind of discontinuous hedging, and give the ratio of risk of several options in American stock market. We can see that the ratio is mostly exceed 5% and the risk of traditional pricing method of option can't be ignored