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## 数学代写|金融数学代写Financial Mathematics代考|Remainder (of the Day) Volume

A related measure that is of real importance in execution is related to estimating the remainder of the day’s volume; how much volume is still expected before the market closes. This is important for sizing the orders to be sent so as to avoid excessive impact. As this will trade into the closing auction, it is important to plan how many shares should be reserved for the auction. We will discuss more of this in the next section.
Denote the expected cumulative volume from time $t$ to $T$ as,
$$r d v_t=\mathrm{E} \sum_{j=t}^T V_j .$$
The naïe approach is to take the estimated volume for next day as $\tilde{V}{T-1}$ based on the data up to the previous day and simply remove the cumulative volume up to time $t$, to estimate the rest of the day’s volume to come, $$\widehat{r d v_t}=\hat{V}-\sum{j=0}^t V_j .$$

## 数学代写|金融数学代写Financial Mathematics代考|Auctions Volume

It is somewhat surprising that not much academic research is available on such an important aspect of trading. Even for practitioners handling the execution of the opening and closing auctions, this is probably a bit more than an afterthought. This is usually handled as part of the volume profiles estimation, in which the opening and closing auctions are respectively the first and last bin of the profile. As per our earlier discussion of volume profiles this ends up being nothing more than an average of the proportion of daily volume. The estimates can be updated intraday using both dynamic volume profiles and rest of day’s volume models as discussed above. More sophisticated approaches leveraging the auction imbalance information that is published by the exchanges (around the last 5-10 minutes of the trading day depending on the exchange) can be used as well.

As mentioned, the current trend towards passive investments and ETFs has driven the liquidity more and more towards the close. This means that the closing auction is becoming increasingly the center of liquidity management. It is quite likely that no other area of research is more relevant and impactful than focusing on better understanding price and volume dynamics during the closing period. In particular in understanding the dynamics in relation to create-redeem activities, across asset classes.

## 数学代写|金融数学代写Financial Mathematics代考|Remainder (of the Day) Volume

$$r d v_t=\mathrm{E} \sum_{j=t}^T V_j .$$

$$\widehat{r d v_t}=\hat{V}-\sum j=0^t V_j .$$

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