I have been following this paper: Price dynamics in a Markovian limit order market, by Rama Cont and Adrien De Larrard
The model is especially pertinent as I only have access to L1 data. The model is clear and intuitive and I have implemented the analytical model. Also it (and the related paper A stochastic model for order book dynamics Rama Cont, Sasha Stoikov, Rishi Talreja) have solutions to key questions like:
- The probability that next move will be an up move.
- The time till the next move.
- Probability of executing an order before the market moves.
Which are precisely the questions I need answers to.
However when I calculate the empirical conditional probabilities of a price movement based on the current book shape (as shown on p12 of the paper), I find that the empirical surface is almost flat (this is based on a months worth of data), suggesting that the current book shape has very little influence on the next tick move?
To calculate the empirical conditional probabilities I simply count up how often each bid/ask size combination occurs and in addition what proportion of these initial bid/ask combinations lead to an up move. (I assume this is correct it should be very simple).
It seems counter-intuitive to me that the book shape shouldn't hold any information regarding the future book movement?
Are there other models that might be better suited to my situation (but that can still allow me to answer the questions shown above?