The Many-World's Interpretion of Jump-Diffusion!

How big was the jump for a given security on a day the asset felt down for example 10% intraday, but in multiple steps? One researcher once told me to simply get hold of all intraday data including volumes and you will know. Sorry it is not that easy, the truth is it depends on what trading seat you are sitting in, and if you not are sitting in a trading seat you basically have no clue at all, I love academics but in this respect you need a trading seat, and every seat will have a different view of reality.

I will like to call this the Many-World's Interpretion of Jump-Diffusion:

No this is not about quantum-finance (that I will leave for another time) . To illustrate my point let’s look at a a naïve example: assume a stock in the morning open at same price as it closed the day before, let us say 100, it trades there for a while then starts to drop, 800 shares trade at 97, 3000 shares at 96, 1500 shares at 94, 450 shares at 92, 4000 shares at 91, 70 000 shares at 90 then the market closes.

How big was the largest intraday jump? The largest jump/gap according to the tape was 3%. But again it depends on what seat you are sitting in, if you have a few hundred shares to sell and got filled at 97 and then looked at the tape you would tell everybody that the largest jump was 3% that day, this is your reality.

If you had one million shares to sell and only got filled on a few thousand hitting all the bids on the way down, and possibly did not even want to show your full size to the market because you knew that would take the market even further down, then the jump was at least 10% today and possibly even larger tomorrow if no sizable bids are coming in.

Even having all intraday trades and all volumes traded the reality of the jump size will be different for different traders. Some factors will always be hidden for researchers that not are closely connected to a trading desk, and even the trader himself can only know the reality of the jump from his own position size and only vague for others.

So how do we then calibrate jump-diffusion models to historical data? It is "impossible" for a outside quant to calibrate your model for you if you are a big player (by massaging the data you can probably calibrate it yoursef), for small players probably okay, and the size do not need to be that big, during my many years in trading (I started as a kid) I have seen some of the world most liquid markets dried up faster than you can count to 3. The market traded but only in the absolute minimum size the market maker had to quote, and some market makers even did not pick up the phone, they were probably hiding in the bath room. What looked like something close to diffusion for some was a massive jump. Only the trader and possibly the market makers could smell what was going on.

Diffusion for some can be jumps for others; it all depends on your trading seat! Historical intraday data can "only "detect minimum jump size they can say littel about maximum jump size, except of course in super liquid market situation where anyone can get filled at almost any price...but in such markets periods there is not much of jumps anyway.

The Many-World's Interpretation applies to many factors in quantitative finance, if you ever run a sizable book in an illiquid market (and even some of largest market's can dry up quickly) you will find out.

This is naturally related to incomplete markets.