modeling - Model reference price of Limit order book

first of all, the description of this Stackexchange forum says its for professionals or academics. I'm doing a lot of self studying and with that I was able to understand some white papers but still I'm neither a professional nor a finance student so please be kind if I'm not using the right terms all of the time. :)

So I'm facing the following problem: I'm just writing a market making bot for a crypto currency and I'm using the Market Making model by Avellaneda and Stoikov. Therefore I need to model the reference price of the limit order book in the first step. Then the bid and ask spread is calculated based on the volatity, drift, trade frequency and the inventory. The reference price and the spreads are then combined to the offers (limit orders) I place.

Currently I'm calculating this reference price by just taking the best bid and ask offer and then calculating the mid of both. However because the book I'm trying do market making in is very thin, there are a few downsides with this method.

1. If somebody places even a very small limit order between the current best bid and ask offer, the reference price shifts in the opposite direction. This is a significant effect if the spread is currently high, which is quite often the case.


2. When for example there is only one large offer which is currently the best ask or bid offer, and this offer is cancled. The price shifts in the direction of the side where the offer was cancled. I could observe this effect in a simulation with real data aswell.

Does anybody know a better way to model the reference price of a limit order book where these affects can be avoided. I have access to level one and level two data of this order book,however Id like to choose the simplest way possible.

Maybe someone has links to helpful white papers or other reference literature, I'd appreciate that too.

Many thanks in advance, Flo

Answer

This reference price is also sometimes called intrinsic price. One of the simplest ways to improve it in regards to the mid-price (assuming you have the depth data) is the following:

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  define a parameter: the size of a hypothetical market order. Let's say it's about the typical sum of first 3-10 order book levels of the instrument;

  
  


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  execute a Buy order with such size against the ask book, and calculate execution price;

  
  


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  execute a Sell order with such size against the bid book, and calculate execution price;

  
  


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  Calculate the intrinsic price as the average of the two prices above;

  
  
  

I assume there are more sophisticated way to define the intrinsic price, but this one already looks much more stable than mid-price, and solves problems 1,2.