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# 数学代写|金融数学代写Financial Mathematics代考|MATH3090 Order Placement

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## 数学代写|金融数学代写Financial Mathematics代考|Order Placement

The order placement layer sits downstream from the scheduling layer and can be termed the micro trader of the strategy. It is in charge of making decisions spanning the next few seconds or next several minutes of trading. In general this layer is not aware of the overall trading intention received by the scheduler. It is only responsible for implementing locally its decisions. More sophisticated methods leverage additional instructions from the scheduler providing a picture on the macro state of the order that may nuance the decision making. In any case, we can simplify the role of the micro trader as answering the question: “at what price should I trade the quantity allocated for the upcoming period to complete the order at the best possible price?” Now we provide the historical evolution of Order Placement techniques.

Naive Order Placement: The simplest approach is to send the given quantity as a market order with essentially no uncertainty in the outcome. The aggregated orderbook (Superbook) can provide a good, conservative (because it does not include the possibility of mid-point hidden orders), estimate of the average price that would be achieved. Depending on the stock and order characteristics the size to trade may still be larger than what can be absorbed by the market without “eating” into the orderbook. This could simply be remedied by decreasing the schedule interval.

The first order placement modules were not that much different from this naïve approach. While for highly liquid instruments with tight spread, this approach may achieve decent results, as we go down the liquidity spectrum, this approach does not work well. One needs to consider the additional complexity that comes with leveraging non-marketable orders.

## 数学代写|金融数学代写Financial Mathematics代考|Peg and Cross

Peg and Cross: The next approach is often termed “Peg and Cross.” It consists of placing a limit order for the scheduled quantity at the near side. If the market moves away, the order can be repriced (alternatively one can rely on a peg order type to do this) and size updated if necessary. If the order is not fully executed by the time the schedule reaches the catch-up zone, an aggressive order can be sent to get back on schedule.

Variations of this approach are still the norm in many order placement products across the industry. An advantage of the approach is that if the order is executed passively on a maker-taker exchange, it will earn a rebate which makes the overall cost of trading lower. On the downside, this technique will consistently be adversely selected with most of the passive executions happening, when the price is “coming through” and is likely to be more attractive right after the order is filled.

One approach to minimize the adverse selection is to “layer” the order book with some of the available quantity so as to capture execution at better prices when they come through. Ideally, with a fast infrastructure, if short term signals like order book imbalance are used to predict when the probability of price drop may reach a critical threshold, the trader can cancel the top order, minimizing the chance of adverse selection. This is a common approach of HFTs as they want to be at the top of the book to capture a fill right before the price moves away.

A common variant of the Peg and Cross technique is to leverage additional price points, in particular the mid-price. As the need for liquidity increases, the order placement can either ping the mid-price of various exchanges or have a quantity hidden at the mid-price to increase the probability of getting filled.

## 数学代写|金融数学代写Financial Mathematics代考|Peg and Cross

Peg and Cross：下一种方法通常称为“Peg and Cross”。它包括在近端为预定数量下达限价订单。如果市场移动，订单可以重新定价（或者可以依靠挂钩订单类型来执行此操作）并在必要时更新大小。如果在进度到达追赶区时订单未完全执行，则可以发送激进订单以恢复进度。

Peg and Cross 技术的一个常见变体是利用额外的价格点，尤其是中间价。随着流动性需求的增加，下单既可以ping各个交易所的中间价，也可以在中间价处隐藏数量，增加成交概率。

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