I center the model on the current atm strike-vol. I then take a range of strikes; 1,2,3 sigmas otm and a 25d as well. I blend the vols to achieve a model of the slope. Honestly, it's not of much use as the skew is so dynamic and dependent on market direction.
Sure, appreciate that, just trying to come up with best practice. No stones left unturned, and all that.
I dont know what products you trade, so I'll keep this general, You should think of two separate components. There is the skew component, which is mostly dependent on the markets perception of the underlying process, and then there is the smile, which is the premium charged by the market for the vol of vol and/or gap risk. The skew component can be modeled in a rather simple manner by something like CEV: Vol(K) = Vol(ATM) * (F/K)^(1-beta) where beta is a constant that was fit to market at some point in time. This way, if you got a true lognormal market (i.e. FX options), beta would be 1, for normal process (i.e. long rates) beta would be closer to 0. You could even have a call side skew (super-lognormal process), for products like gold and other commodities. The vol of vol modelling is a different story and there is a bunch of ways to do it. The real question here is - what are you doing? if you are making markets, you want one thing, if you are trading prop, you want something else. ps. I hate the new bloomberg keyboard
Equity index options (FTSE100). Prop trading and here is exactly what I'm after..... When I enter a new spot price into the BS model, it will generate a new option price. However, the assumption is a flat vol surface which isn't correct. What I'd really like, is the BS model to calculate an option value taking into consideration how the IV will change as the underlying moves across the smile. gbos has suggested a model (looks very good) but my initial thoughts are that it would generate circular references when incorporated in the BS model, but I've not got to work on it yet. To all intents and purposes I could just forget about any skew and just assume that the smile is symetrical, otherwise it could get incredibly complicated ! Ideally it would be great to have a stand-alone formula that would adjust the BS derived option value for vol smile. I bet there isn't one !
SABR will bring nirvana to you. You can find a summary paper for example here http://www.riskworx.com/insights/sabr/sabr.html. In short, you calibrate the skew and curtosis parameter once in a few month and only adjust the alpha based on ATM volatility. Correct delta and vega dynamics are guaranteed.