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MTH9879-Market-Microstructure-Models

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A collection of homeworks of market microstructure models.

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# MTH9879-Market-Microstructure-Models
## Homework Collection: Market Microstructure Models
MTH9879 Market Microstructure Models is a graduate course for students of Baruch MFE Program. All homeworks is done in Jupyter Notebook with R.

The course covers but not limits to the folowing topics:

- Market mechanisms
 - Theoretical and empirical models of the order book
 - The market/limit order decision
 - Inventory models
 - Rational expectations and models of strategic trading
 - Market making
 - Sequential trade models
 - Understanding the bid-ask spread
 - Variance and covariance estimation
 - The long memory of order flow
 - Models of market impact
 - Market impact of meta-orders
 - Price manipulation
 - Optimal execution strategies
 - Modeling latency
 - Optimal order routing algorithms
 
 
 
### Lecture 1: Market mechanisms and zero intelligence models of the order book
 
 - The limit order book can be viewed as a complex queuing system.
 - Even with very simple rules, complex order flow and price dynamics can be generated.
 - With more realistic rules, zero-intelligence models of the order book can serve as useful tools for comparing the performance of proposed order execution strategies.

Homework 1 is related to this lecture.
 
 
 
### Lecture 2: Order book and order flow: The market or limit order decision
 
 - Parlour (1998) shows that a rational market order/ limit order decision should depend on the state of the order book
 - Foucault, Kadan and Kandel (2005) model the order book as a market for immediacy, relating the spread to the ratio between patient and impatient traders
 - Rosu (2009) removes many over-stylized features of FKK (2005) by allowing instantaneous cancelation of orders
 - Cont and Kukanov (2013) show how to incorporate the fee structures and current queue lengths in different venues to optimize the market/limit order mix.
 - Bouchaud, Mezard and Potters show that the average order book shape, consistent with ZI simulation and empirical observation, may be derived using a simple price diffusion approximation
Mike and Farmer find a simple empirical relationship between the arrival rates of limit and market orders

Homework 2 is related to this lecture.
 
 
 
### Lecture 3: Inventory models and market-making
 
 - All inventory models have the following characteristics:
    - It is optimal for the market maker to keep inventory close to zero.
    - There will therefore be market impact
       - Market sells cause the price to decrease.
       - Market buys cause the price to increase.
    - The spread is compensation for risk.
       - The spread is increasing in volatility and in the price of risk.

- In real markets, as in Guilbaud and Pham, as in the case of big tick stocks, the spread is given.
    - A market maker either joins or improves the best quote, or does no business.
 - Market order arrival rates are not symmetric: they depend on the book imbalance.
    - Cartea, Donnelly and Jaimungal solve an optimal control problem to find the optimal placement of limit orders using the book imbalance.

Homework 3 is related to this lecture.

### Lecture 4: Understanding the bid-ask spread

Homework 4 is related to this lecture.

### Lecture 5: Price formation under asymmetric information: The Kyle model

- In economics, the role of prices is not just to allocate resources efficiently but also to transmit information about the values of assets.
 - The Kyle model exhibits a mechanism through which information may be impounded into market prices.
    - Note however that the market price can depart very substantially from fair value if there is large uninformed demand.
    - If fair value is itself evolving dynamically, the market price may never correspond to fair value.

Homework 5 is related to this lecture.

### Lecture 6: Variance and covariance estimation

- There has been a huge expansion in the literature on realized variance and covariance estimation since around 2003 with many very interesting papers.
 - As a result, we now have very efficient estimators for realized variance that take into account all of the available information.
    - The newer volatility estimators are all very much more efficient that RV sampled every 5 minutes.
    - Moreover, kernel-based estimators are easily updated in real time by adding the most recent tick and dropping the oldest tick.
 - The article by McAleer and Medeiros is a nice review of the literature up to 2008 or so.
 - The rough volatility forecast seems to be the simplest and bes.

Homework 6 is related to this lecture.

### Lecture 7: Long memory of order flow and market impact

- Order flow is a long memory process.
    - The dominant effect is order-splitting.
 - Market impact is concave due to selective liquidity taking.
 - Market impact of market orders can be modeled as:
    - Permanent but state-dependent (Lillo)
    - Transient (Bouchaud)
 - Both of these formulations are equivalent.
 - To get quantitative (as opposed to qualitative) agreement with observation, in principle we need to take into account
    - Time-varying liquidity
    - Limit orders and cancelations
 - In practice, it seems (see Taranto) that distinguishing between market orders that change the price and orders that result in no price change is enough for a surprisingly accurate description of market impact.

Homework 7 is related to this lecture.

### Undergraduate Version

The undergraduate version of this course is a series of selected topic in market microstructure and is taught by Prof. Tai-ho Wang at Peking University. This folder contains homeworks and solutions of this course.