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Intraday scatterplot of DAX-future against the DAX volatility index VDAX

Fig.1 shows an intraday scatterplot of the DAX future against its volatility index VDAX on 6-Jan-2016.

The data suggest a strong negative correlation between the two.

There are various models available that "describe" this effect: For example stochastic vol-models such as the Heston model. However these models only describe but do not explain the effect.

Since prices are the result of trading and market-making, a plausible explanation could be that market participants are buying put-option when the market goes down in order to protect their (long) position thereby driving the vol up; and re-selling them when the market goes up (driving the vol down).

However it is easy to convince oneself that the correlation persists at time-scales that correspond to vol moves that make it difficult to trade out of the bid-offer spread of the option (at the ODAX-exchange). If it was only to reduce the downside risk (in a down move) it would be much cheaper to reduce ones long-position temporarily instead. Clearly options exhibit "gamma", but (as mentioned above) the cost of gamma seems too high given the bid-offer spread of the options.

So I do not really understand which market factors cause this intraday phenomenon of negative correlation between vol and spot moves.

Can anyone suggest an answer?

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This effect is coming from the supply and demand in the options markets. Many portfolio managers want (or need) to buy out of the money put options, and many are willing to sell out of the money call options (thereby funding the purchase of put options). Now, when the market goes down, dealers find themselves short vol and they need to buy options to cover (hence vol goes up). Likewise, when the market goes up, dealers find themselves long vol and they need to sell (thus vol goes down). That's the effect you observe. The timeframe for this effect is almost continuous - many dealers recalculate their positions multiple times intraday.

Yes, there is a skew whereby out of the money puts are more expensive than ATMs and out of the money calls are cheaper. You can think of this as compensation for the expected hedging loss if you are using a simple Black Scholes model. However, many dealers would use a model that anticipates the vol change for the given market move. This model would price the puts and calls closer to the market skew. It would also reduce the losses from flattening the vol position after a market move. As for the question about bid-offers, it is an issue, but in practice a dealer won't just lift and hit in the market. They will rather work to buy and sell close to mid market, which they can probably do using their network of clients.

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  • $\begingroup$ Thank you, I am grateful for your reply ! A consequence of your explanation , given that the volatility-skew has become a fact of life , is that the dealers are sitting on negative gamma-positions on vol: According to what you are saying, they need to sell vol at times when it tends to be low (because spot is going up) and need to buy when vol is expensive (markets go down). My follow-up question then: $\endgroup$ – user3072048 Jan 7 '16 at 10:05
  • $\begingroup$ How do those dealers get reimbursed for this negative vol-gamma position? Does it come from the extra premium they are making from the volatility skew when selling the out-of-the money puts? And how do they deal with the high bid-offer spreads in the market? A second follow-up question: Occasionally the relationship of negative correlation breaks down (markets going up and vol is increasing ). Do you have any intuition what could be going on in this case? Many thanks $\endgroup$ – user3072048 Jan 7 '16 at 10:05
  • $\begingroup$ A scenario where the market is going up and vol is increasing: let's say the market has been stable in a range for a while and suddenly the Fed eases rates and the market goes up 3% in a day. It would be likely that vol would go up, due to anticipated further large moves. $\endgroup$ – dm63 Jan 7 '16 at 11:40
  • $\begingroup$ thank you! As far as my conclusion is concerned based on your answer provided; namely that the (downside) skew is essentially a kind of "option-premium" reimbursing the dealer for neg-vol gamma, would you agree? $\endgroup$ – user3072048 Jan 7 '16 at 12:06
  • $\begingroup$ sorry for my last question; didn t realize you had answered above (: $\endgroup$ – user3072048 Jan 7 '16 at 12:47
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A large part of this comes from the simple combination of: 1. A downward sloping volatility skew (which corresponds to a skewed risk neutral distribution) 2. Sticky strike behaviour

The vol that you plot is not for a fixed strike but ATM, which has a strike that follows the spot.

You would observe this pattern even if there was no spot/vol correlation, just by the way you read off bol numbers from a skew.

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I think there is something that has not been mentioned. "price" is used as the x variable instead of "change in price" or return. This could be a problem, as price itself is non stationary, causing problem to statistical properties. With that being said, correlation is an inflated indicator here, exaggerating their relations. In Heston's model, indeed, the correlation is between return and volatility change.

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  • $\begingroup$ thanks ! Can you explain what an "inflated indicator" is ? (or a link would be perfect) $\endgroup$ – user3072048 Jan 11 '16 at 13:49
  • $\begingroup$ basically it means that if the true correlation is 0.5, the calculated correlation could be 0.8 which is much higher. You can check "pseudo regression" as reference. $\endgroup$ – Daniel Jan 11 '16 at 17:19
  • $\begingroup$ let me try to understand: You are saying that the plot presented above could be misleading because the DAX on the x-axis is not stationary and hence linear relationships that may arise may be spurious in nature; along the lines of Granger and Newbold (in their seminal paper) ?. $\endgroup$ – user3072048 Jan 11 '16 at 18:31
  • $\begingroup$ yes, that is what i mean. $\endgroup$ – Daniel Jan 11 '16 at 18:39

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