Is there an error in this? "In this case book pressure is simply (99.0010 + 98.755)/(10+5) = 98.9167." in the Market Structure signals section. I can't see how that equation relates to the trade data given just prior.
> Let two players each have a finite number of pennies (say, n_1 for player one and n_2 for player two). Now, flip one of the pennies (from either player), with each player having 50% probability of winning, and transfer a penny from the loser to the winner. Now repeat the process until one player has all the pennies.
> The chances P_1 and P_2 that players one and two, respectively, will be rendered penniless are
> P_1 = n_2 / (n_1 + n_2)
> P_2 = n_1 / (n_1 + n_2)
So if the current order book looks like:
- Sell 5 for $99.00 (best offer)
- Buy 10 for $98.75 (best bid)
And you chomp up orders randomly, flipping a completed order to the opposite position:
- the probability that the price is above $99.00 (all 5 sell got filled first) is 10 / (5 + 10)
- the probability that the price is below $98.75 (all 10 buy got filled first) is 5 / (5 + 10)
So expected value is (99.00 * 10 + 98.75 * 5) / (10 + 5) = 98.9167.
I am not happy with this explanation. It seems like after you execute an buy for $98.75 you need to immediately put a sell for it at slightly above $98.75 (and vice versa) to fit the random walk model described above. And then I took the expected value using the price at two different points in time. Overall I am still confused myself.
