The Cont model describes ahighly liquid stock that nearly always trades with a bid-ask spread of onetick.  Treating the size of the bid-queueand the size of the ask queue as two (uncorrelated!) random walks with identicalvolatilities, prove that if the current size of the bid-queue is X and thecurrent size of the ask-queue is Y, then the probability the next price changewill be “up” is given by: