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Modelling Skew
- Thread starter Profitaker
- Start date
Quote from Profitaker:
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).Quote from sle:
I dont know what products you trade
Prop trading and here is exactly what I'm after.....Quote from sle:
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.
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 !
Just had a little play - that looks very good !Quote from sle:
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.
Quote from Profitaker:
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 ! [/B]
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.
Many thanks. I'm going to re-read it another 20 times.