Stochastic control models for optimal liquidation of a large block of stocks

Abstract

The liquidation of a large block of financial assets naturally arises from numerous financial practices, such as, executing orders, hedging large portfolio of derivatives and deleveraging. Fast liquidation depresses the share price significantly (market impact), while slow liquidation may expose to the risks of potential price fluctuations as well as inability to fulfill the liquidation obligation within time limit. Accordingly, it is inevitable to large financial institutions to strike a balance between market impact and other potential risks rising from liquidation. The popularity of electronic trading system further stimulates the thirst for developing automated trading program under some optimality criteria to give guide to traders. In this thesis, I study the optimal liquidation problem in the context of continuous time models based on a stochastic control approach. Due to regulatory issues, it is typical for large financial institutions to liquidate parts of assets in order to meet the predetermined capital requirement set by regulators or leverage ratio target set by managers. This motivates studying the objective of maximizing the probability that the final cash position exceeds some preset benchmark (abbreviated as outperformance probability). An alternative criterion of maximizing the expectation of the liquidation revenue in excess of the benchmark is also proposed in order to take account of tail behavior of revenue distribution. I formulate the optimal liquidation problem under above two criterions as two stochastic optimal control problems. I also derive the governing Hamilton-Jacobi-Bellman (HJB) equations that characterize the value functions based on the weak dynamic programming principle of Bouchard and Touzi [9]. The spatial boundary conditions of HJB are further derived to complete the formulation. The finite difference method and policy iteration algorithms are proposed to solve for the value functions as well as the optimal execution rates. Finally, comprehensive numerical experiments are conducted under two different cases: liquidating an illiquid stock within one month and liquidating a liquid stock within one trading day.

Date of Award	2016
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology