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We perform numerical simulations of the limit-order driven Sergei Maslov (SM) model and investigate the probability distribution and autocorrelation function of the bid-ask spread S and the quote-update frequency U.For the probability distribution, the model successfully reproduces the power law decay of the spread and the exponential decay of the quote-update frequency. For the autocorrelation function, both the spread and the quote-update frequency of the model decay by a power law, which is consistent with the empirical study. We obtain the power law exponent 0.54 for the spread, which is in good agreement with the real financial market.