This paper presents a novel stochastic agent-based model for limit order books (LOBs) that bridges the gap between pure agent-based and pure stochastic approaches. The model features two types of liquidity-motivated agents: liquidity providers (market makers) who submit and cancel limit orders, and liquidity demanders who place market orders. The agents' activities are modeled using multivariate skew-t distributions to capture heavy tails, skewness, and non-linear dependencies across different LOB levels and event types. The model is calibrated to high-frequency Level 2 data from Chi-X using a combination of indirect inference and multi-objective optimization, allowing it to replicate both price and volume dynamics. The authors demonstrate the model's practical utility by simulating the impact of a regulatory quote-to-trade ratio, finding that such a measure can reduce extreme intra-day volatility. This framework provides a rigorous tool for testing exchange regulations and informing trading strategies, with the flexibility to incorporate additional agent behaviors or market rules.