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.