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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:

$\text{OOI}_{it}=\frac{\sum_{j=1}^{N} 100\text{ Dir}_{itj}\text{Delta}_{itj}\text{Size}_{itj}}{\text{Num_Shares_Outstanding}}$

Where, The option order imbalance,$\text{OOI}_{it}$, is measured for stock i on day t. $\text{Dir}_{itj}$ 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.$\text{Delta}_{itj}$ is the option price sensitivity to the underlying stock price, and $\text{Size}_{itj}$ 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? $\endgroup$ – Bougias A. Sep 19 '18 at 20:36
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There are two main types of orders: limit orders and market orders.

Limit Orders:

Limit orders are passive orders that are placed on the book at a given price, and remain there until they are executed or cancelled.

Market Orders:

Market orders are executed immediately at the best available price in the book, against a limit order that is already there.

Imbalance:

When we talk about book imbalance, we are looking at the imbalance between bid and ask prices, thus we are looking at the imbalance between limit orders. However, when we say trade imbalance, we are looking at the imbalance between market orders. Trade imbalance gives us a more "real-time" indicator of the trading direction, and also a stronger signal about informed traders' decisions.

Dummy Variable:

When you say "buy trades and sell trades cancel out", you actually mean a limit order and a market order have different directions (one is buying, the other is selling or vice-versa). However, when you want to know towards which side the market is actually moving, you want to know the aggregate direction of the market orders. This is why you need the dummy variable to indicate if it is an aggressive buy (market order to buy being executed against a limit order to sell) or an aggressive sell (market order to sell being executed against a limit order to buy).

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