Equilibrium Models of the Limit Order Book
Open Access
- Author:
- Wei, Hongxu
- Graduate Program:
- Mathematics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 04, 2021
- Committee Members:
- Iouri Soukhov, Major Field Member
Alexei Novikov, Major Field Member
Alexei Novikov, Program Head/Chair
Alberto Bressan, Chair, Minor Member & Dissertation Advisor
Bing Li, Outside Unit, Field & Minor Member - Keywords:
- Limit Order Book
Nash equilibrium
Repeated game
Infinite time horizon
Informed agents - Abstract:
- The thesis mainly studied different equilibrium models of the Limit Order Book (LOB). And it contains two main parts. The first part starts with a "one-shot" game, and it shows that the two sides of the LOB are determined by the distribution of the random size of the incoming order, and by the maximum price accepted by external buyers (or the minimum price accepted by external sellers). Then the model is extended to an iterated game, where more agents come to the market, posting both market orders and limit orders. Equilibrium strategies are found by backward induction, in terms of a value function that depends on the current sizes of the two portions of the LOB. The existence of a unique Nash equilibrium is proved under a natural assumption, namely: the probability that the external order is so large that it wipes out the entire LOB should be sufficiently small. The second part introduces models in the infinite time horizon, allowing for random fluctuations in the fundamental value. Firstly, we consider when all agents have the same information, but the external players may anticipate a random jump in the value of the stock, and what is the difference between the model with constant fundamental value and with a random jump in the fundamental value. Another part is considering two different cases: if the agents posting limit orders are risk-averse; and if some of the external agents have the information that there will be a jump in the fundamental value. We are curious about how the shape will be changed under these two cases.