Question

Black Scholes and Binomial Trees are widely used by industry players. However, what makes these models far from perfect?

Answer 1

Black Scholes is far from perfect because:

1. It assumes no early exercise (for e.g., fits only European options)—the model is unsuitable for American options.
2. It assumes no dividend payout, ignoring the impact on the change in valuations.
3. It assumes stock prices to follow lognormal pattern, for example, a random walk ,ignoring large price swings that are observed frequently in the real world.
4. It assumes continuous and costless trading, ignoring the liquidity risk.
5. It assumes constant values for risk free rate of return and volatility over the option duration, none of it may remain constant in the real world
6. Other assumptions like no penalty for short sales, no arbitrage opportunities and no taxes, but in reality all these do not hold true because realistic profit potential is decreased.

Binomial Trees is far from perfect because:

1. It takes longer to value the option because the calculation will take longer than other models if one is looking at a lot of options.  
2. A key limitation is that the actual prices of options contracts are determined by market forces, not by formula no matter how sophisticated the formula may be.
3. There is a problem with its complexity. An enormous number of calculations and variables are necessary when calculating potential options prices.

And this is the reason why both the models are far from perfect.