Lookback option is a well-known path-dependent option where its
payoff depends on the historical extremum prices. The thesis focuses
on the binomial pricing of the American floating strike lookback put
options with payoff at time $t$ (if exercise) characterized by
\[
\max_{k=0, \ldots, t} S_k - S_t,
\]
where $S_t$ denotes the price of the underlying stock at time $t$.
Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and
Vorst} (RBCV, 1992) who proposed a transformed binomial lattice
model for efficient pricing of this class of option, this thesis
extends and enhances their binomial recursive algorithm by
exploiting the additional combinatorial properties of the lattice
structure. The proposed algorithm is not only computational
efficient but it also significantly reduces the memory constraint.
As a result, the proposed algorithm is more than 1000 times faster
than the original RBCV algorithm and it can compute a binomial
lattice with one million time steps in less than two seconds. This
algorithm enables us to extrapolate the limiting (American) option
value up to 4 or 5 decimal accuracy in real time.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3075 |
| Date | January 2007 |
| Creators | Wang, Xuyan |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | 593753 bytes, application/pdf |
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