### 金融代写|市场微观结构与算法交易代写Market Microstructure and Algorithmic Trading代考|QF302

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

When it comes to intraday trading strategies we have the following dilemma, also known the trader’s dilemma: If we trade slow then prices will move away from their current quote, i.e. we are facing a market risk; however, if we trade fast then our order will drive quotes away from the current one, i.e. we will have a great market impact (see Figure 1.4).

Recall that in MPT we optimize the joint effect of two oppossite forces: minimizing the risk of the portfolio and maximizing the (expected) return. Following the idea of the efficient frontier, it seems natural to build up a optimization program that minimizes simultaneously both market risk and market impact.

Suppose we need to sell a certain amount of asset $S$ during the day. We split the trading order in exactly $N$ small sub-orders of size $\nu_n, n=1, \ldots, N$. The goal is to find the right trading proportions
$$\nu_i \geq 0, \quad i=1, \ldots, N ; \quad \sum_{n=1}^N \nu_n=1,$$
that minimize the expected loss due to market risk and market impact.
As we will see in later chapters, the set of minimizers constitute a curve, the optimal trading curve. For a given risk level (variance), the trading strategy $P$ on the optimal trading curve is the one that minimizes the expected market costs, i.e. the joint effects of market risk and market impact (see Figure 1.3).

## 金融代写|市场微观结构与算法交易代写Market Microstructure and Algorithmic Trading代考|The scope of this m´emoire

The goal of this mémoire is to describe thoroughly the construction of the optimal trading curve $\left(x_0, \ldots, x_N\right)$ for different market models and portfolio strategies.

In Chapter 2 we will study the market microstructure. We will see how the hypotheses of MPT and CAPM, i.e. the Efficient Market Theory, are all violated in real markets. We will focus in particular on the effect of transaction costs and market impact. We will also review the benchmarks used for monitoring trades.

Roughly speaking, a trading strategy is algorithmic if it is stripped of human decisions (and emotions). In Chapter 3 we will describe what is algorithmic trading. We will survey the basic strategies in algorithmic trading, which are the bricks with which almost any systematic trading strategy can be constructed. We will also show evidence that favors algorithmic over human trading.

In Chapter 4 we will construct the optimal trading curve $\left(x_0, \ldots, x_N\right)$ under normality assumptions, i.e. where the asset follows a Brownian motion. This chapter will be based on the article of Almgren and Chriss [1] for single assets and on the work of Lehalle [14] for multi-asset

In Chapter 5 we will construct again the optimal trading curve $\left(x_0, \ldots, x_N\right)$, but following Lehalle [14] we will consider that the portfolio has mean-reverting dynamics. We will solve analytically and numerical a simplified case of a mean-reverting portfolio using the shooting method, which is a numerical technique used in differential equations. The novelty of our approach is the alternative optimization program we use: we will construct the optimal trading curve using 1-dimensional algorithm regardless of the total number of trades $N$. Being more advantageous than the classical approaches based on functional optimization in $\mathbb{R}^N$, this approach could be of interest for systematic brokers and traders.

Chapter 6 is the final chapter. We will make some remarks on the portfolio models we have presented and mention some possible extensions. We will also review several alternative models for time series that could be used to describe markets more accurately. Finally, we will comment on the pros and cons of automated (algorithmic-based) trading with respect to discretionary (human-based) trading.

# 市场微观结构与算法交易代考

$$\nu_i \geq 0, \quad i=1, \ldots, N ; \quad \sum_{n=1}^N \nu_n=1,$$

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