Understanding volatility skew
Can't understand this phenomenon. Is it because of psychological forces causing people to demand more for put options due to valuing protection against downside more than benefitting from upside from out of the money calls. Is there a mathematical explanation or is it more sentiment? Also, how does this reconcile with the Black Scholes formula? Appreciate the help.
I have always understood it as being caused by the fact that in equities changes in volatility are negatively correlated with changes in the underlying. So in equities when prices move down, vol jumps. When prices move up, vol is flat/slightly down depending on where you are coming from. Ask yourself when looking at a vol smile graph, what would realized vol be if the underlying moved to that far out of the money put strike price? What would peoples forecast for future vol then be?
Thank you
not always, many single stock names have moved spot up, vol up and vice versa over the last yr
Yes, all aspects of the investment universe do not follow the exact same rules of thumb at all times. Did you know that one time supply of an item decreased, demand stayed the same, and prices went down at first? Did you know that one time wheat futures moved up 0.25% and implied vol on the 10 delta call went up?
Stock indices drift up, crash down. The average volatility on a downward path is higher than the average volatility on an upward path
Thanks - but why doesn't the incredibly lower probability of drastic downward move factor in? Does the magnitude of downward correction overpower the lower probability?
Skew does account for higher magnitude/lower probable events: if you look at the corresponding probability density function for a vol smile with "negative" skew (skew for puts over), then you will see the downward movements are larger in magnitude, but less frequent/occur with lower probability.
The smile can evolve for both empirical and supply/demand reasons... However, I think equity index skew first arose historically from demand for downside put protection - I don't think many people at the time were looking at empirical vol data at different values of spot/fwd.
edit: Black-Scholes assumes a flat vol smile (i.e. vol does not vary with strike/spot) - this is one of the assumptions that isn't true in practice
https://quant.stackexchange.com/questions/51519/how-does-volatility-ske…
I don't think there is an obvious theoretical explanation for why volatility skew exists in US equities and not in all markets although clearly corporate mergers are going to be a much larger factor in the vol curves of single stock options as a typical merge offer will be associated with a sharp price increase and then volatility decrease. Neither of those empirical facts are incorporated in Black-Scholes which is certainly a very basic model that is now often used for implying implied volatility for options even though the varying volatilities produced by those implications are clearly inconsistent with the original modellng assumptions.
Arguably risk aversion whether justified in utility terms or due to psychological factors and the demand for options/dynamic hedging/panic selling are all important factors as well. It's also probably empirically the case in US equity indices that there are more margin calls when the price decreases rather than decreases and unlike cash equities there don't seem to any significant short squeezes like Volkswagen in 2008.
Whatever the still somewhat unclear reasons for the historic 20% drop on Black Monday in 1987 that day also seemed to have a big impact on the volatility skew as there has never been a similar up move. I have not personally verified this but there are certainly claims that the volatility skew was much less pronounced before then. At this point it's an empirical fact that as another posted noted "stock indices drift up, crash down" but I don't think there is unambiguous theoretical explanation for why this is the case. From the perspective of market makers selling out of the money puts or outright volatility is generally considered to be positive EV but sufficiently risky that such trades are not worth doing at all or only doing in very small size so few or no market participants are going to be trying to flatten the volatility skew.
Hi, there are a number of reasons. One, large non-hedging holders buy puts as protection, and sell covered calls to monetize their longs. This natural buying pressure of lower strikes and selling of upper strikes can create a skew effect. But more importantly for me, I delta hedge. The general relationship of spot vol is inverse. If I’m selling otm puts, I would expect realized volatility to increase as the spot gets closer to the strike. My short gamma also grows in this scenario making each larger daily move more costly for me. So I better charge a higher premium to compensate me for that risk. Likewise you’ll see higher call strikes have higher vol in take out candidates. In one day that 40% otm call could be itm and I’m dead.
I understand how covered calls work with fully funded long stock positions but how does it work for US equity index options? For SPY I imagine it's straightforward in the same way it is for cash equities although SPY options are relatively less liquid and I am not sure that many traders/institutions are holding fully funded long SPY positions in any case. At CME I believe there is some cross margining between ES futures and options but an ES covered call seems like by put call parity it would be equivalent to a selling a put on ES where you are exposed to margin calls as ES declines due to the futures position which is never going to be fully funded like a cash stock. Presumably short ES positions combined with selling out of money ES puts would be similarly cross margined. I believe CBOE SPX options are the most liquid and presumably the most complicated from a covered calls perspective as the options are cash settled unlike the underlying cash equity positions. The COBE website https://www.cboe.com/tradable_products/sp_500/spx_options/ seems to indicate there is some margin offset for SPY or IVV positions in qualifying accounts but is that really a significant influence on out of the money SPX calls given total SPY + IVV AUM is around 1.2T ~ 2% of total SPX market cap?
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