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Currently studying the paper:

HU, Jianfeng. Does Option Trading Convey Stock Price Information?. (2014). Journal of Financial Economics. 111, (3), 625-645. Research Collection Lee Kong Chian School Of Business.

To test the impact of option order flow affects stock order flow. Author defines the measure of option order imbalance:

$OOI_{it}=\frac{\sum_{j=1}^{N} 100 Dir_{itj} Delta_{itj}size{itj}}{Num\_Shares\_Outstanding}$

Where, The option order imbalance,$OOI_{it}$, is measured for stock i on day t. $Dir_{itj}$ is a dummy variable equal to 1 if the jth option trade on stock i is initiated by the buyer, and -1 if the trade is initiated by the seller, according to certain trade signing algorithms.$Delta_{itj}$ is the option price sensitivity to the underlying stock price, and $size_{itj}$ denotes the trade size in option lots (100 shares of the underlying stock).

My question is:

If option trade denotes an executed trade, why do we need the dummy variable? Shouldn't buy trades be cancelled out by sell trades? Since whenever one buys someone else sale the respective quantity( price differs due to bid-ask spread).

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    $\begingroup$ It is true that "for every buyer there is a seller" so buys always equal sells. But by "order imbalance" in these types of studies is meant an excess of buyer-initiated trades, which is thought to be bullish. The classification of trades (based on who initiates it) makes it possible to test if this is true. $\endgroup$ – Alex C Sep 19 '18 at 19:50
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    $\begingroup$ So, we select realized trades (not placed orders) using historical data of the trade and classify them based on the price executed according to the signing algorithm? $\endgroup$ – Coxswaiiiin Sep 19 '18 at 20:36

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