Order book characteristics and the volume-volatility relation: Empirical evidence from a limit order market

Randi Næs, Johannes A. Skjeltorp

Journal of Financial Markets (2006)

• Introduction: 

1. While on average about 50 percent of the order volume for NHY has limit prices which lie within 5 ticks from the quoted spread, the similar number for OPC is only about 10 percent. 
2. Overall, we find that there are systematic variations in the order book slope across securities and over time. 
3. The main contribution of the paper is to identify strong evidence that the order book slope is negatively related to both trading volume and price volatility, as well as to the correlation between volume and volatility. 

Fig. 1 shows the total and visible order books of the two largest and most liquid securities in our data.

• 過去對於Volume-volatility關係之解釋： 

1. The main theoretical explanation for the relation is that the arrival of new information makes prices adjust to new equilibria over time. 
2. A complementary explanation is that prices also change because investors have dispersed beliefs about asset values. 

• order book slope與volume–volatility關係的可能解釋：

1. To investigate further the relationship between the order book slope and the volume–volatility relation, we study factors that interact with the order book slope.
2. A significant negative relationship is found between the order book slope and the coefficient of variation in analysts' earnings forecasts, i.e., the greater the disagreement among analysts, the more gentle the average slope of the order book.
3. This result suggests that the order book slope proxies for dispersed beliefs about asset values.
4. Applied to the two securities in Fig. 1, this would imply that investors disagree more about the value of OPC than NHY.
5. However, our results could also be explained within a Glosten (1994) model with homogeneous liquidity suppliers.
6. In the Glosten model, different order book shapes arise because liquidity providers condition their limit orders on the probability of informed market orders.
7. Hence, for a given level of liquidity-motivated trading and a given probability of informed trading, the slopes will be more gentle the more volatile assets are.
8. We also find that smaller firms have order books with a gentler slope than larger firms.
9. Assuming that there is more private information in smaller than in larger firms, the gentler slopes in small firms may indicate that there is a greater pick-off risk in these firms.

• 委託簿斜率之衡量：

價格彈性 = (△Q% / △P%)

彈性是根據每日的六個不同時間點所計算：10.30am, 11.30am, 12.30pm, 1.30pm, 2.30pm and 3.30pm


The more gentle (steeper) the slope, the more widely distributed (concentrated) the volumes in the order book are.

• 委託簿斜率的含意：
• As there are no theoretical models available that address the relationship between the order book slope and the volume–volatility relation, we approach the task of interpreting our results indirectly by investigating empirically what factors can explain variations in the order book slope. 
• 分析師盈餘預測變異 (意見分歧) 
• 交易者人數：愈多人想交易，則下單必須較為積極才有機會成交，因此斜率愈小

• 實證結果：

• 交易的競爭人數愈多，斜率愈小
• 意見愈分歧，斜率愈小

• 結論:

Our findings are consistent with models where the volume–volatility relation is partly explained by dispersion of beliefs.

1. First, a more gentle order book slope (i.e., greater dispersion of beliefs) increases volatility and trading activity. 
2. Second, a more gentle slope also coincides with a stronger correlation between volume and volatility 
3. Our results point out several directions for future research on limit order books.
4. One interesting question is whether the systematic variations found in the shape of the order book reflect heterogenous beliefs or asymmetric information.Examining how the shape of the order book is affected by public information disclosures or other events that align investors' beliefs and information could provide important insights into this question. 
5. The indeterminate causality relationship between order-book slope, trading activity and volatility is another interesting topic for further work.