我們建立了在限價委託簿(limit oeder book)上以雙向拍賣制度(double aucton)運作的代理人基模型(agent-based model)。初步透過無策略的的代理人與具有羊群效應(herding effect)的代理人進行模擬交易比較，在具有羊群效應的模型中我們設定以決策後選擇市價單(market order)的代理人會出現羊群效應。羊群效應即是個體因從眾心理而表現出來的群體一致性行動。在金融市場中，即是交易者們受到過往市場價格變動的影響而產生決策收斂做出相同動作的現象，當市場價格波動越大時，一致性會越明顯。由於市場交易者各自有著不同的操作週期，所以模型中也考慮了交易者具備不同長度的歷史價格變動記憶。基於真實金融數據做統計分析後得到的典型事實(stylized facts)，如價格波動的厚尾分佈(fat-tail distribution)和volume imbalance等，在我們的模擬結果也能得到。從結果來看，羊群效應確實可以造成更劇烈的價格變動，且記憶長度越長時，價格變動(volatility)也越劇烈。另外我們發現了一些新現象，在價格變動的自相關(autocorrelation of volatility)分析上，價格變動的記憶效應遠低於交易者對價格變動的記憶長度，我們認為這可能是來自於限價單(limit order)的影響。另外在volume imbalance和價格獲利率(price return)的關係上，羊群效應降低了在small imbalance時產生大價格變動的機會。在初步的模型中也無法得到如真實市場的spread-volatility關係，對此我們亦認為可能是受到限價單置放到限價委託簿上的方式所影響造成。於是我們比較了三種不同機制所得的結果，第一個機制即羊群效應，第二個機制是限價單的置放位置會受spread大小的影響，第三個機制則是交易活動熱烈程度會與過去的價格變動大小呈正相關。

We build an agent-based model of an order-driven market with double auction. At first, we start with the comparison of non-interaction agents with no strategies and the herding agents who submit market orders. The simulation results reproduce some stylized facts
such as fat-tailed distribution of volatility and volume imbalance. The herding effect is implemented by aggregation of agents who take market orders into opinion groups. The number of opinion groups in a simulation step is determined from previous volatilities of the
market as different agents compare the price change over different time intervals. Besides confirming that when herding is included the tail of the distribution of volatility is enhanced, we found several new results. First, the autocorrelation time of volatility is much shorter than the memory of most of the agents because limit orders have strong influence on the location
of best bid and best ask. Second, from the relation between bid-ask imbalance and price return we find that herding reduces the chance for a small imbalance to produce a large price change. We find that the relation between spread and volatility in our preliminary model
does not agree with empirical data, we think limit orders have strong effects on the stylized features. Next, we compare the effects of three mechanisms. Our first mechanism is opinion aggregation, i.e., herding of agents in response to price volatility in the market is studied.
The second mechanism is the way that limit orders placed by the agents are affected by the size of the spread in the limit order book. The third mechanism is the enhanced trading activities in the presence of large volatility.

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