This paper presents a comprehensive parametric model for simulating limit order books, focusing on the intensities of order flows. The authors model market orders, limit orders, and cancellations as point processes with intensities that depend on the state of the order book, specifically the spread and volume at the best quote (for market orders) or total volume (for limit orders). The intensities take an exponential quadratic form in the logarithms of these variables, ensuring non-negativity and enabling efficient maximum likelihood estimation. For cancellations, a novel 'priority index' is introduced, representing the volume ahead of an order in the queue, which effectively captures the selection of orders to cancel. Limit order placement is modeled using a Gaussian mixture distribution, allowing for multi-modal patterns observed in empirical data. The model is estimated on high-frequency data from six liquid stocks on Euronext Paris over ten trading days. Results show that the proposed intensities fit empirical patterns well, including the decrease of market order intensity with spread and the increase of limit order intensity with spread. Simulations demonstrate that the model reproduces key stylized facts of limit order books, such as the distribution of spreads and volumes, outperforming a standard Poisson benchmark. The work provides a flexible and realistic framework for limit order book simulation, useful for market microstructure research and practical applications.