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.