Hi, can anyone explain why volatility skew tends to flatten out as time goes by?Thx

You are translating prices (market or model) through the BS model, which is based on GBM.Let's say the model matches the market, so we can talk about the market.Pick a market, expiration, and moneyness where there is a significant skew, say SPX striking 15% down from current levels in 4wks.The implied vol is around 30% compared to around 15% atm.A 15% down move in the SPX over 4 wks would represent a 'significant' move in the statistical sense based uponthe atm vol of 15% (annualized).But, if you fix that moneyness level (-15%) and then simply extend the maturity, eventually you reach a maturity wherea move to that level is simply 'ordinary' not 'significant'. So, the implied vol for that level will be much closer to the at-the-money IV. (Of course, the atm IV itself may be much higher or lower at that distant maturity --- but that is a separate issue). In any event, the skew (at a fixed moneyness) has then flattened. So, by this argument, the flattening is simply due to the spreading out of the risk-neutral pdf in time, which is a very weak and typical property.

Alan just following on from your response, can we link it to vol being proportional to square root of time.So difference between 1y and 4y expiry..vol should be roughly double.Ok sorry this has no impact on flattening of skew..Now that I type this I realize that this is not really the emperical case or perhaps has no theoretical grounding either, so how does this relationship come about on a vol surface?On a random note, Is forward skew equity derivative lingo for higher strikes exhibiting higher vol than lower strikes?

any comments please, on this time-vol relationship?thanks alot

You can explore it by the following method, say for SPX. Fit Gatheral's SVI curve to various option expirations.With that, you can construct smooth risk-neutral pdf's. Measure their std. devs as a function of T.

There are two principal factors involved in the IV skew that you should take into account before reading any significance into any remaining skew. First asset price dynamics tends to be geometrical. Second, std dev increases as sqrt(T). To see if there is really any remaining skew and how it evolves with T, then instead of plotting IV against strike, try plotting your IV against[log(strike/spot) - rT]/[minVol*sqrt(T)]where r is the risk-free rate and minVol is the lowest IV value on your plot.You will see that most of the flattening disappears. In fact, if you plot all expirations on top of each other on the same graph, they may be pretty much indistinguishable (apart from the extended range of the shorter expirations). Edit: Actually you'll get a better match between expirations if you replace r by the rate at which the strike at the smile minimum moves with expiration.