Volatility Smile Interpolation Model

Options priced by the Black-Scholes formula are quoted on the market by implied volatility. In other words, to price an interest rate European option, one needs to know forward rate, the strike level and volatility along with the discount rate. However, the market trading history has shown that it is not perfect to trade options solely based on the Black-Scholes model, simply because there are many other factors that falls out of the model assumptions.