PhD Thesis Proposal Defence


"Numerical algorithms for exotic financial derivative"

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 rate, 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
tailored-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
folds. 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 proposal, 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, is proposed to model the path dependent structure in an option
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 behavior is revealed by a dynamic programming
algorithm which compares the early exercise value and continuation value
at each grid node in the lattice tree that simulates the stochastic
dynamics of the risky asset.  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 analyze
non-tradable employee stock options with reload provision.  Finally, we
consider the liquidation problem where a trader seeks for an optimal
trading scheme to unwind a huge portfolio within a time constraint.  We
conjecture that the proposed numerical algorithm framework is capable of
solving such problem.


Date:     		Monday, 8 December 2003

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

Venue:                  Room 2406
			lifts 17-18

Committee Members:      Dr. Mordecai Golin (Supervisor)
			Dr. Yue Kuen Kwok (Supervisor/MATH)
                        Dr. Cunsheng Ding (Chairman)
			Dr. Siu Wing Cheng
			Dr. Samuel Wong (ISMT)


**** ALL are Welcome ****