Some thoughts on options contract IV (Implied Volatility) differing from RV (Realized Volatility)

In post https://www.dhirubhai.net/posts/shanmukham-kumarappan-a38137136_are-developed-markets-really-more-efficient-activity-6862080090340233216-YrZ8 Shanmukham Kumarappan asked why IV (Implied Volatility) tracking with RV (Realized Volatility) tends to be a bit noisier & looser than in India.

Below is my response, which is just one person's perspective, and I probably have mistakes herein, but so what. Perhaps not really a discussion for LinkedIn, but oh well. I'm a little rusty on options and on market microstructure, so take my OPINIONS with a grain of salt.

Implied Volatility is NOT reality. You probably already know, and may take for granted, that IV is the number you get when you iteratively re-run BSM (Black-Scholes-Merton) with a varying range of IV and you stop when the IV value you plugged into BSM gives you the current price of that option. Imagine if you pulled a stunt like this in any other profession. This almost sounds like fraud. However, over time it tends to be a reasonable approximation MOST OF THE TIME. If I recall correctly (?) it tends to do a worse job when the markets start straying out towards the fat tails of volatility.

Disclaimer: my next comment could be outdated since I've not looked at multi-exchange market-depth price displays for options in 10 years: Separately, when IV gets published for options, you need to read the fine print about which exchange, and for what level of market depth, and for what time of day, and from which price was IV calculated.

(This is easier to explain with a whiteboard, but oh well.) "Price" first gets divided into trades vs quotes(bids/offers). Trades are backward looking and are supposed to be ironclad historical and immutable facts. For the sake of present discussion, let's assume that is accurate. Quotes (bids/offers) is where funny business starts to enter the picture. BBO (Best Bid & Offer) is the mid-point of the entire order book on a single exchange. NBBO (National BBO) is the mid-point of a list aggregating the order books from all exchanges. The inside spread may have only a light amount of size associated with that price.

Trading firms in well-funded bulge bracket firms may have some trading desks which don't depend on IV published by an exchange or data vendor. Rather they may recalculate on an intraday basis what is IV at that moment. That may cause their IV to bounce around (Volatility of Volatility ?). That might cause their trading signals to provoke more reactions per day. Such reactions include changes to their market orders(quotes) with a small fraction of those orders(quotes) resulting in actual trades.

While they are doing this, their quotes and trades are seen by competitors who respond by changes to their market orders(quotes) with a small fraction of those orders(quotes) resulting in actual trades. As if that weren't confusing enough, each of these competing trading firms might post orders(quotes) on different exchanges for the exact same instrument, but possibly at different price levels. Some of those order(quotes) are not left posted long enough to actually get traded, but are only a subterfuge to get detected by competitors' computers but withdrawn before competitors' computers can execute but may still cause competitors' computers to change their analysis of the market.

To achieve all these manipulations requires insanely fast networking between each of the exchanges and each of the trading firms. Sometimes this means the trading firm renting server rackspace inside the exchange datacenter. However, how can that trading firm put that same server inside two different exchanges' datacenters. Mostly they can't (though some exceptions ). So, the trading firm puts one server at one exchange and another server at another exchange. Then the trick becomes how to connect that one trading firm's 2 servers together to have a shared view of the aggregated overall market.

That leads us through the looking glass into Alice in Wonderland, or When the speed of light is NOT speedy enough: Light and electricity travels about 11.7 inches per nanosecond in a vacuum. Electricity on a shielded trace on a PCB slows down to about half that, or ~6 inches per nanosecond. This is already too much verbosity for LinkedIn so I'd encourage you to read "Flash Boys" by Michael Lewis for further details on why & how trading firms spend so much money on faster networking.

Now, IV can only be calculated once you decide WHICH price you want to use for the calculation. Different people have different but valid reasons for choosing a different price (trade/bid/ask/close/open/high/low) when they calculate IV. As if that weren't confusing enough, there are critics of BSM who might choose a different model, such as Binomial (Cox Ross Rubinstein)

All my above comments and your original post assume option contract IV & price are considered only in the context of a "naked" options position. However, MANY MANY traders construct a position using a basket or multiple legs of options. {Sometimes they are constructing synthetic futures (google it). Sometimes those synthetics are for the sake of backing out some constituents from an index futures position.} Regardless, when creating a multi-legged position, you often can't wait for your preferred price for each leg of that position. So, either you do the best you can, or you give up and forget about putting on that position at that time.

If you accepted inferior prices for one of the legs of your position, guess what? That now becomes part of the trade history for that one options contract, which is a price that gets written in ink. If that price sets a new BBO or OHLC, then that inferior price can skew the published IV.

Point being, looking at the price (& IV) of a given options contract in isolation without considering larger context around all the different users of that instrument, may lead to puzzlement such as expressed in the original post.

So, how much weight should you give to published IV when comparing against RV ???

You can probably guess my view if you've read this far.

Your comments and opposing viewpoints are welcome. Let's just keep it civil.