Question

Why would the black scholes merton formula give a different value for the option price then the actual price?

Answer 1

There are several reason as to why the option price from BSM Model differs from the actual price. Some of them are as follows:

1. The interest rate is assumed to be the Risk Free Rate in the model, however, in real world interest rate changes rapidly.

2. Model assumes that only Eurpoean Options are exercised but in real world stock exchange, American options are traded which can be exercised anytime during the life of the options.

3. It also assumes that market are perfectly liquid, which is ofcourse not the case in real world.

4. This model assumes that the stock price follows normally distributed, however, risky securities have fat tails and negatively skewed.

5. Volatility is assumed to be constant in the model, but, in real world it can vary and does not remain constant.

6. The model also assumes zero dividend paying stocks, however, in real world stock do pay dividend which changes stock price and inturn changes the option price.

7. Arbitrage opportunity might/sometimes exist in the real world, which is again is not in line with the model assumptions.

8. Also, there are Transaction Fees and Broker Fees while trading stock options in real world.