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# SK10 vs 25D RRN

Discussion in 'Options' started by VolSkewTrader, Jan 28, 2019.

So I ran the SK10 calculations for WTI Crude Oil - SK10 = [Vol(ATM) – Vol(ATM – 10%))/sqrt(DTE). I have a real-time data grid that shows me the Normalized 25D RR [IV(25delta) - IV(75delta)] / IV(50delta) live for every automated curve fitting publication. Although I think the SK10 helps characterize the downside skew across all expirations of the terms structure, it only tells half the story. Because the SK10 measure only includes the downside strike (which may be appropriate for stocks or equity indexes), if there is a flattening or steepening slope in the calls (like we see in commodities or FX) then one measure may conflict with the other, which it does in this case.

According to the SK10 calculation, My front month expiry Mar19 has the most negative SK10 figure (-.206) vs the further out months, implying that its put skew is the steepest vs the ATM, which it is. However, my Normalized 25d RR reading of (-7.37) shows that Mar19 has the flattest overall curve when comparing the OTM 25d puts vs the OTM 25d calls. This is due to the OTM calls (upside strikes) trading much higher vs the ATMs in Mar19 relative to the other further out expirations.

It's clear that the Normalized 25d RR indicates a more accurate picture of the overall slope and shape of vol curve across all months under one product. The SK10 measure only gives me relevant information for half of the vol curve. Is there an SK10 formula that includes upside strikes? What would be the mathematical formula for the correct moneyness for an upside strike (OTM call) for a log-normally distributed underlying. What would be the SK10 equivalent for an upside strike? It would have to be some strike more than (>10%) 10% OTM, or less than 90% moneyness.

TheBigShort likes this.
2. ### sle

I think I wrote a bunch about it before, but here it is again. Each measure has it's positives and negatives.

Delta-based skew measure (RR/ATMF) is the "purest" measure of skew, but because you are re-scaling by the ATM volatilities. Most FX people use it because it naturally assumes a sticky delta type of behaviour and it's very easy to recover you risk reversal once you update the ATMF.

Fixed strike skew measure (SK10) is most useful in equities that have flat skews and very little smile to them. Since most of demand for vol in equities is from hedgers and most supply is from overwriters, the linear model is very handy. For example, it's consistent with the expected vol dynamics - assuming some constant multiplier, you can easily estimate expected increases in fixed strike vol when the market moves.

Finally, to your problem of oil. Thinking about the skew in non-spot assets (such as oil) is very tricky. The ATMF vol is actually an average of expected paths of volatility that would take into account the increase in vol as the futures approaches expiration. Since volatility on a commodity is time-to-expiry dependent, while the skew is not, it makes measures like RR/ATMF overestimate the skew for long-dated expiration. Fixed strike measure would have different issues, since both strikes are undergoing the roll to spot and the evolution of the skew in time will be f*cked up.

3. ### TheBigShort

@sle answer is very thorough, but could you provide the data you used for the sk10 calc? Preferably csv

4. ### nooby_mcnoob

I understood some of these words

Onra likes this.

Thank you for the clarification. Most of what you say makes perfect sense. I think the delta based skew makes most senses for floating skew commodities such as crude and grains. Not sure if vol or skew is time-to-expiry dependent. Like any other traded instrument, the vol, term structure, and skew for commodities are completely dependent on the directional behavior and velocity of movement of the underlying. On vol exploding market drops, along with term structure, the skew will steepen, sometimes dramatically in favor of the downside strikes (puts), negating any drop in vol due to the floating skew behavior, where high skewed puts slide their way down the curve. On vol-imploding rallies, its just the opposite, the OTM puts (downside strikes) get destroyed relative to the OTM calls, which can flatten the skew dramatically. The OTM calls can even catch a strong bid if the rally continues past retracement levels. The calendars and term structure probably behave just like any other product.

Interesting to note that equities have predictable expected increases in fixed strike vol when the market moves. Probably something you have taken full advantage of. Not sure this is quantifiable in commodities, which are more unpredictable.

Sure. I just ran my numbers on excel. these were done last night during a quiet evening session. Here they are:

Expiry DTE Spot Price 90% Strike ATM IV 90% Strike IV (ATM -10%) SK10 calc Normalized 25D RR
Mar-19 17 52.09 46.88 35.90% 40.90% -0.206 -7.37
Apr-19 46 52.37 47.13 35.15% 37.48% -0.158 -9.15
May-19 78 52.71 47.44 34.98% 36.70% -0.152 -9.27
Jun-19 108 53.05 47.75 35.89% 37.33% -0.150 -9.49
Jul-19 140 53.36 48.02 35.65% 37.02% -0.162 -9.84
Aug-19 170 53.58 48.22 35.48% 36.72% -0.162 -10.48
Sep-19 199 53.72 48.35 34.90% 36.03% -0.159 -10.84
Oct-19 232 53.78 48.40 34.12% 35.21% -0.166 NA
Nov-19 262 53.8 48.42 33.42% 34.50% -0.175 NA
Dec-19 291 53.8 48.42 32.87% 34.09% -0.208 -12.24

Hope that is helpful.

TheBigShort likes this.
7. ### sle

Well, look at vol in Mar and look at vol in Dec, which one is higher and why?

Vol has come down from multi-year highs (seen late last year),and along with it the inverted steepness of the calendars (in vol terms). If we continue to trade sideways or see a slow grinding rally, Mar vol could easily print lower than Dec vol with the term structure steepening toward the further out maturities. In a low/falling vol market, Dec vol will likely be higher than Mar or any other month that expires before it.

Dec (and further out LEAPS) vol hardly moves, and stays anchored within an extremely tight range. This is likely the case for all exchange-traded products.