Need some help!

I have calculated the theoretical price of an index option using BS and Binomial models and are now comparing the three. While BS and Binomial have approximately the same value, market price is way off. The Option is an European index option and assuming no dividends. 

The difference between Market and BS/binomial should stem from binomial assuming markets are perfect (no commissions, bid-ask, etc) 

BS assumes constant risk free rate and volatility. Other problems are estimation of volatility and that BS assumes no large shifts.

Can you think of any other reasons why they are different? The reason I am asking is that I feel market and the theoretical is too far apart. Binomial and Bs differ slightly from each other, but that is probably because of the number of steps I have used. 

Thanks for your help. Scrolled through this site now and its nice of the contributors to 
help all the random people. Hopefully I can contribute some day as well! 

Steven