i dont do much with retail type clients but from what i have seen most individuals who speculate in options markets tend to do it from a short vol perspective ("look at all this yummy premium I am getting paid") hence the long gamma comment.
if you want a decent mid- level treatment of financial math the most user friendly text out there is probably paul wilmott, derivatives. anyone with undergrad stats will easily get thru it and find it provides, more importantly than the math, an intuitive grasp of the concepts.
back to the original question though, i seriously dont think you get a huge benefit from using anything more sophisticated than black-scholes even for american options as long as the underlying meets the obvious criteria. i have access in my job to quite a few different models but we tend to use black scholes (albeit with minor fudges) for pricing individual vanilla positions, for pricing the overall portfolio of risk simulations are a major test to make sure the trading desk view of net risk is supportable, especially if the book includes any non-vanilla positions. much more value added (in a trading sense) comes from making serious attempts to model a volatility term structure as this is where opportunities to take a sensible view are greater, in its basic form its not even complicated, the first input is just a look at the calendar and assigning weights to various days which will likely have an effect on volatility.
if you have a supportable view that the market (or more happily, a client!) is mispricing volatility thats much more important than the choice of model you are using to price options or determine implied vol. if the approach to estimating your parameters is internally consistent value then becomes relative rather than absolute. everyone on the street now has access to the same technology so relying too heavily on a particular model leads you unwittingly down the path of model arbitrage which usually means a looming road accident. in the real world, adjustments and fudges to simpler models based on previous experience (usually negative) or fear of future uncertainty (ie scary what ifs - what happens if we get a 5 sd event - shouldnt happen even once in our lifetime yet i can think of several in the last 10 years in the fixed income world without even trying. at the end of the day actual volatility cannot be determined and future volatility cant be predicted.
perhaps the most honest statement (and maybe the only one) you'll ever get from the investment banking world is that past performance is no predictor of future performance. funnily enough, that is also the most likely statement to be ignored by investors.
one last thought is that the biggest search in finance (in the new brave world of less prop trading and more fee based income) is not necessarily the search for better technology, but the search for new clients who dont have access to your existing technology...... the excessive personal returns in investment banking referred to elsewhere on this site still happily exist but they are going to a smaller proportion of employees, and certainly in US firms, an icreasing percentage of comp is being locked up in 3 to 5 year vesting schemes. bring back the early 90s!
i'm not sure if thats helpful to you but regardless, i've finished thinking about work this week, after finishing last night at midnight its now my weekend!
