Stock price changes with market impacts and its application for pricing derivative securities

根据东京证交所各股票的每日收盘价序列估计的市场影响程度与其交易量回归。发现这种关系是清楚的。相同股票的报价数据大约在同一时间公布。通过仔细检查报价数据，发现从封闭价格序列计算的市场影响的大小大于市场上观察到的买卖价差。这种差异预计来自一个特殊的市场微观结构有关的收盘价。强烈的负序列相关性被发现在日经225期权的隐含波动率的日序列在OSE。这一点太强烈了，无法用买卖价差来解释。基于期权理论价格的虚拟机械交易可以产生巨大的超额收益。这一事实有以下两个含义：1.根据历史股价序列计算的股票期权理论价格比根据普通历史波动率计算的股票期权理论价格更接近市场实际价格。然而，这种配合在香港市场上相当不错，但在OSE中却不令人满意。我们的工作可能表明存在的异常在OSE。如果是这样的话，历史股票价格数据可能有助于预测正确的市场期权价格，这是非常有用的市场参与者。作为本研究的副产品，作者发现了一个空间选择模型，成功地解释了Duverger定律。这有望为一个悬而未决的问题提供重要的解决方案。

The magnitude of market impact estimated from the daily closed price sequence of individual stocks on the TSE is regressed on their trading volume. The relation is found to be clear. The tick data for the same stocks are published around the same time. By scrutinising the tick data, it is found that the magnitude of the market impact calculated from the closed price sequence is larger than the bid-ask spread observed in the market. This difference is expected to come from a special market market microstructure concerning the closing price.Strong negative serial correlation is found in the daily sequence of the implied volatility of Nikkei 225 options on the OSE. This is too strong to be explained by the bid-ask spreads. Virtual mechanical tradings based on the theoretical option price calculated by GARCH type models are found to produce huge excess returns. This fact has the following two implications:1. Theoretical stock option prices calculated from the historical stock price sequence is known to give better fitting to the actual option price in the market than those calculated from the ordinary historical volatility. However, this fit is fairly nice in the Hong Kong'market, while it is not satisfactory in the OSE. Our work might suggest the existence of anomaly in the OSE.2. If so, historical stock price data data might useful in predicting the correct market option price, which is very useful in the market participants.As a by-product of the present research, the author found a spatial election model which successfully explain the Duverger's law. This is expected to give an important solution to an open problem.