Here's an answer to a question I posed to a quanty fellow who's doing a little retail options trading prior to the job hunt...he's at another board. (question went something like, "math..hm?" "Options is based on Black-Sholes. BS is a calculus formula. Hence options is based on math. Now, how much math you need to know is a different topic. Sky is the limit. My feeling is the more math and statistics one knows, the better one understands options. Now, someone will argue that knowing math/stats does not make someone a good options trader. Fair enough because trading is about risk/money management too (see Taleb, etc.). But I think not knowing the math/stats will make someone a bad trader because that person does not understand option pricing and hence does not understand fully the instruments he is trading. I say learn as much as math/stats as you can but don't be fooled into a false sense of security by knowing math/stats. After all, market movement is determined heavily by mass psychological forces." Sounds fair enough, eh?

all true, but one must also keep in mind that Black-Sholes is only one of many formulas and none of them hold true, just as CAPM, the accepted academic calculus for stock pricing does not hold.

First of all, Black-Scholes assumes log-normal probability distribution, which does not hold in reality, so even if you can derive the B-S in your sleep it will still fail you in the real world. Hence, options trading is not all about a pricing model. Besides, you don't need a PhD in Maths/Statistics to understand option pricing.

Correct, although it helps if you are a quant developing pricing models for exotics, seeking closed form solutions, etc. You can very easily get an intuitive feel for option pricing, risk-neutral valuation and equivalent martingale measures from the simple binomial model, and you don't need heavy duty stochastic calculus for that. Check out http://www.amazon.com/exec/obidos/t...002-9789300-4596807?v=glance&s=books&n=507846 it is written by Neil Chriss from Goldman Sachs, and is one of the best for building your intuition with regards to this sort of thing. It rips on the standard intro text (which is the piece of rubbish written by J Hull). IMHO. Of course if you wish to really get into math fin, have a look at Karatzas and Shreve. That should give you an indication of the level of mathematics expected if you wish to get very formal. Remember, bog standard Black-Scholes-Merton makes far too many basic assumptions (do Volatility smiles mean anything to you? And this is only one of the problems), and these things are used to price derivatives. Don't confuse pricing with trading. A good trader using Black-Scholes-Merton will outperform a crap trader using cutting edge stochastic volatility models.

To understand B-S you need enough probability theory to know what "log-normal" means; and you need introductory differential calculus to understand what the greeks mean.