The Hong Kong University of Science and Technology
Department of Computer Science


PhD Thesis Defence


"Numerical algorithms for exotic financial derivatives"

By

Mr. Ka-Wo Lau


Abstract

A financial derivative is a financial product or contract whose value
depends upon other underlying variables, which may be the prices of traded
securities, stock indices, 3-month interest rates, etc.  There has been a
phenomenal growth in the number and variety of derivative securities
traded in the markets.  New exotic derivative products that are
tailor-made to meet the individual needs of clients are constantly being
invented. The construction of the theoretical framework for the pricing of
new derivative securities has been one of the major challenges in this
area.

The complications of pricing exotic financial derivatives come in two
ways. First, the value of a financial derivative may depend on a complex
path-dependent structure.  Second, some financial contracts come with an
early exercise right which permits the holder to exercise the right before
the maturity.  In this thesis, a general numerical algorithm framework is
proposed to value exotic financial derivatives which exhibit
path-dependent structures and early exercise rights.

First, the forward shooting grid approach, characterized by the
augmentation of an auxiliary state vector at each grid node on a lattice
tree simulating the stochastic dynamics of underlying variable, is
proposed to model the path-dependent structure in a financial contract.
The versatility of the approach is demonstrated by applying the method to
price some path-dependent options such as Parisian options, reset options,
and alpha quantile options.

Second, the early exercise feature is tackled by a dynamic programming
algorithm which compares the early exercise value and continuation value
at each grid node in the lattice tree. We propose to combine the forward
shooting grid technique and the dynamic programming algorithm to analyze
the pricing behavior, optimal calling policy, and optimal convert policy
of convertible bonds.

Furthermore, we propose to extend this approach to value and analyse
non-tradable employee stock options with reload provisions. Under the
utility maximization approach, the risk aversion, personal wealth of an
employee, and the reload rights outstanding will enter into the pricing
algorithm. The pricing model is then applied to examine the impact of
compensation incentive of the reload feature to different types of
employees.

Finally, we consider the liquidation problem where a trader seeks an
optimal trading scheme to unwind a huge portfolio within a time
constraint. Subject to the execution time lags and liquidation discount,
we propose a numerical algorithm to compute an optimal trading strategy
such that the terminal expected value of riskless asset is maximized.


Date:			Saturday, 4 September 2004

Time:			10:00a.m.-12:00noon

Venue:			Room 1504
			Lifts 25-26

Chairman:		Prof. Chang Tai Hung (HUMA)

Committee Members:	Prof. Mordecai Golin (Supervisor)
			Prof. Yue Kuen Kwok (Supervisor)
			Prof. Cunsheng Ding
			Prof. Lixin Wu
			Prof. Mike K. P. So (ISMT)
			Prof. Peter A. Forsyth (Comp. Sci., Univ. of
						Waterloo)


**** ALL are Welcome ****