Which of the following option pricing model are most commonly used in trading US stock and index options? 1) Black-Scholes for American options (continuous dividends) 2) Cox-Ross-Rubinstein Binomial pricing algorithm 3) Barone-Adesi-Whaley / Quadratic approximation (continuous dividends) 4) Bjerksund and Stensland (continuous dividends) 5) Roll-Geske-Whaley (1 dividend) Which of the above is more accurate and why? Thanks in advance...

I don't think in today's market any textbook model is used without modifications. Most trading companies are utilizing proprietary implementations of published models. As for accuracy; download 5 to 10 different implementations of each model and plug in the same variables. Now lets see how many produce the same answer ...

I've only heard it referred to as "Binomial Pricing (American)". I have an algorithm in C (if you're a programmer) that comes pretty damn close calc'ing an option (puts and calls). You have to provide the spot price, strike, interest rate, volatility and time to maturity and the algorithm will spit out a price. If this is useful to you, let me know.

How do you incorporate fat-tails in a model? I used Black Scholes to play around, doing what-ifs, using Excel (can even do limited Monte Carlo) but have been trying to figure out how to incorporate a fat-tails model. I greatly appreciate any help I can get.

You need to relax the underlying distribution assumptions. Unfortunately, that immediately makes any such "solution" vastly inferior to Black-Scholes due to its analytical and computational complexity. However, there are lots and lots of things that people have come up with. Various jump diffusion type approaches are probably the best known among them.

Not trying to create a complex algorithm, so is there a simple analytical equation approximation (as opposed to lognormal) I can try, just to play around for general strategy and trends?