Why do implied volatility changes at different strike prices exactly coincide with one another?

Question

Please see the image of the Implied volatility of different strike prices separated by 100 points. This is the recorded data of the actual market.

As it can be clearly observed that the Implied volatility of all strikes moves almost with 1 correlation. But the market activity during different strikes was very different. The market volumes were high at the strikes 15600CE and 15700CE. And the Volumes at 15400CE were very low. It seems that the Implied Volatility is manipulated. Please explain why this high correlation is seen in the market.

Answer 1

It does not suggest manipulation. To quote another answer:

The efficient market hypothesis implies that the key driver of stock price changes is not trading volume but predictive information.

The same goes for options. Many options rarely trade, but their bid and ask quotes are nevertheless continually updated by a market maker based on a pricing model. The implied volatility (IV) you plotted may be based on the bid and ask, not just on actual trades.* Or, if the time intervals on the chart are long enough that trading is occurring at all strikes but simply much more at some than others, then it is still true that low volume doesn't prevent prices from shifting quickly.

When expectations shift toward large moves (for stocks in general or this stock/index in particular), IV tends to increase at all strikes simultaneously. Option pricing models incorporate typical relationships of IV among strikes, such as the volatility smile.

*In this case, even though the IV may not reflect actual option trades, it is a real indicator: Offers for potential trades were present with that IV, and the fact that trades didn't happen shows that market participants agreed the IV was fair (to within the market maker's spread). For example, if the quoted IV were way too high compared to a consensus value, then traders would have been selling the option and bringing down the market maker's price.

Answer 2

If it were not related, you would get lots of arbitrage opportunities. This answer shows how to use SVI to fit a vol surface from market quotes.

If you look at these two fictional examples, you will realize that one has several mispriced options, while the other has all options more or less aligned with the entire vol surface.

Now in reality, you face issues like stale prices, unreasonable small or large bid/ask spreads, you need figure out a way to handle that the underlying asset and options on the asset can trade during different times on different exchanges, that there exist erratic prices, especially close to the opening and closing times of the trading session...

That is why actual shapes of IV surfaces are quite fascinating at times. Voladynamics has some great examples on their webpage.

The underlying message is the same though: IVs must be related to each other, otherwise there will be arbitrage opportunities. Since there are many firms constantly monitoring this, any such opportunity will be very short lived.

In my opinion the cleanest way to show why this makes sense is to look at FX OTC options. It is a very liquid market with lots of market makers constantly quoting implied vol for At-the-Money Delta Neutral Straddles, Risk Reversals and Butterflies for several deltas. Combined, they give you the entire Vol surface. In a nutshell,

• ATM determines the level (you can think of it as the Black Scholes IVOL for a specific tenor),
• RR the skew (how its tilted, towards OTM puts for RUB and GBP in the examples below) and
• BF the kurtosis (how pronounced the general wings are).

Getting call and put IV from these quotes requires a combination of these using the following relations:

• RR = C - P (for deltas)
• BF =(C + P)/2 - ATM
• C = ATM + BF + RR/2
• P = ATM + BF - RR/2

Plotting this you can see how they depend on each other:

It is changes in ATM vol that move the entire surface up and down. The vol surface (smile, smirk, skew,...) exists mainly because there are fat tails, skewness, heteroscedasticity, jumps (crashes), and so forth. None of these real-world phenomena are featured in the Black Scholes formula. The market just developed ways to account for many of the shortcomings of Black Scholes.

Now, equity is not vol quoted (at least not exchange traded / listed options). However, the general idea is the same. In fact, some market makers even quote IV surfaces for equities alongside variance swap rates. If you have access to Bloomberg (many universities and libraries like the New York Public Library have Windows PCs running Bloomberg Terminal software), you can look at OVDV to see FX quotes and the surface I displayed above. If you have access at work, you will likely also have access to some OTC IV quotes for equities on OVDV (just select the dropdown where BVOL stands to switch quotes).