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

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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.