THESIS
2016
xii, 59 pages : illustrations ; 30 cm
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 liqu...[
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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.
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