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Hi,I am trying to estimate the time until a stock order gets filled. E.g. I place an order in t0 for price P0 in the market and know at this time the amount S0 of orders that are before me in the que. I would like to estimate in t>t0 the time that is left until my order gets filled. If I would know that the price of the stock is constant I could use a moving average of placed orders and estimate the time until the amount S0 becomes 0.Since the stock price is stochastic the price I have placed in the market is not guaranteed and my order might get delayed. Any ideas how to approach this problem and embed the stock price movement as a stochastic process, if possible in an analytical solution? I know about hitting times of stocks to certain barriers but are not sure if this can be applied here.Thanks and regards

As you probably know, there is an analytic formula forthe probability of a Brownian motion (with volatility sigma) to hit a barrier adistance x away prior to some time t. As a first appraoximation, this would seem to be what you need.I would try that formula with (i) no drift, and(ii) take x to be the absolute return (as a decimal) corresponding toa move from the current price to one tick away from your price.In other words, the market trades through your price. If the stock is optionable, you could use the shortest dated optionimplied volatility (with the strike closest to your limit price) for sigma.regards,