Latent order books + reaction–diffusion model

1:47:53So I I was reading this and I was like, okay, I I would like to know mechanistically though what's going on. >> Right. >> Okay. I'm a physicist. It's like what's actually going on, >> right? >> Right. >> Because there's clearly some underlying >> Yes. The underlying physics that's there. >> There's there's some explanation. >> That's none of these other things. >> Yes. Okay. So the victor comes from something called latent order book models. Okay. This is from Bousard Doniier and Mastrom Mateo in 2015. Buchard actually holds a PhD in theoretical physics from ENS which is like the um you know top university in Paris and his analogy is um reaction diffusion in chemical reactions. Okay,

1:48:33imagine you've got two different types of particles. You've got a biparticle and you've got a cell particle. If they meet up they annihilate, right? So they they they they poof out of existence, right? The by particles are on one side and the cell particles are on the other side. Okay? And they all want to get to each other, but because of the nature of the reaction in the middle, there's not going to be any because if they were in the middle, they would annihilate, right? So, you're going to get a density profile that is roughly linear >> on the right hand side and the left hand side. And I think the next picture shows this very well, which is the density profile being comp like very much linear. So you're asking for a certain

1:49:15price above the current price and that's the that's in the red. So this is like this is like how much I would sell for. >> Yes. >> And then in the blue is how much I would buy for. >> Mhm. >> And it's roughly linear. >> Yes. >> Right. Okay. So now imagine with this linear sort of density profile of my um order book. These are the order books. Right. Suppose some order of size Q comes in. Okay. How much of it is going to go away? It's going to be that triangle. >> Mhm. [clears throat] >> Right. >> Mhm. >> And what's the area of the triangle? The area of the triangle is 1/2 times the

1:49:58length and the width. Right. So it's it's the total size is my area and that's proportional to the price impact squared. I'm so >> so the price impact is proportional to the area square root. >> Yep. >> It's it's a >> it's strictly universal. >> It's like it it like makes sense. It has to do with the shape of the >> Yes. >> of the or of the order book, >> right? >> Right. The area is the price impact squared. >> Yes. >> And so the price impact is the area square root. And the area is the size of your order. >> So can we all go home? >> It's [laughter] like pretty simple. I thought that was like kind of cute.

1:50:39>> No, that that is that is because it it it you know there's all a lot of always a lot of handwaving. Yeah. The thing I love about F it's like no but like like >> Yeah. How how does it work though? >> Show me like don't well like we have to you know some risk of >> Yeah. No, it's like no just oh it's okay. It's [laughter] just an area. >> That's why you guys don't want to talk about it because you're trying to take your premiums because then because you know anyway. >> Yeah. >> Um >> that was this is actually really cool. econo physics. >> Yeah. Yeah. It I thought I thought, you know, and it makes sense then now that it was it was in PRL. It's a pretty cool study like the way that they batched the orders together to like figure out what the trading desk was doing, things like that. I I think I think it was a really

1:51:20cool study. um you know the practical impact I don't know somebody's probably going to make billions in slippage yeah based on this or it's probably going to be priced in because now this is now that this it's it probably already is priced in because like the economists don't actually care about like the the finance guys don't actually care about the underlying like oh why is it doing it's like oh it's already been an empirical observation so they're going to put it in their algorithms anyway so you know I I don't know if like >> you're going to make a lot of money off this insight but it's a cool insight nonetheless This is not financial advice. >> No. [laughter] Yeah. Yeah. Don't go do experiments. Hey, I wonder if I buy a 100 Bitcoin, what's going to happen? [laughter] >> We're just some physics nerds over here.

1:52:01Okay. So, uh, >> don't come cry. No, that's actually that's because I think you can find there's structure all around us. Yeah. Right. Right. >> Exactly. Yes. There's structure all around us. And it's it's it's accessible, but it is not it's sometimes maybe a little opaque >> or or or or discreet in terms of how we engage in a like move around in the world >> and then how it becomes obvious. >> That's a very good point. There is structure all around us. I like that. >> It's it's and I mean this is through all