Does Black Scholes model work in real life?If no, what are other better Option Pricing Model(s)?
No, it doesn’t. It assumes that volatility is constant for options of all strikes on the same underlying with the same time to maturity. We can see that in the real market this is not the case: If you examine the prices of options traded in the market, compute the Black-Scholes volatility from the price (the so-called “implied volatility”), you find experimentally that in nearly all markets it is not constant. The general pattern is that options that are “at the money” (i.e. their strike is at the time-discounted price of the underlying security) have lower implied volatilities than other options, while far in-the-money and far-out-of-the-money options have higher volatilities. This pattern is called the “volatility smile”. A number of models attempt to match the volatility structure of the market to get better prices. Examples are the Dupire model, and the Hull-White series of models.
