CS-98-05: Abstract


DISCRETE PARISIAN AND DELAYED BARRIER OPTIONS:
A GENERAL NUMERICAL APPROACH

K.R. Vetzal
Centre for Advanced Studies in Finance
University of Waterloo
Waterloo, ON
Canada N2L 3G1
Telephone:  (519) 888-4567 ext. 6518
E-mail:  kvetzal@watarts.uwaterloo.ca


P.A. Forsyth
Department of Computer Science
University of Waterloo
Waterloo, ON
Canada N2L 3G1
Telephone:  (519) 888-4567 ext. 4415
E-mail:  paforsyth@yoho.uwaterloo.ca


In this paper we present a numerical method for the valuation of derivative
securities which have a payoff dependent upon the amount of time during
the life of the contract that some underlying variable lies within a
specified range.  We concentrate in particular on the examples of Parisian
options and delayed barrier options, but our approach is easily adapted
to other cases such as switch options and step options.  Available
analytic pricing formula are based on the assumption that the underlying
variable is monitored continuously.  In contrast, we consider discrete
(e.g.\ daily or weekly) sampling.  Given that path-dependent option values
are known to be generally very sensitive to sampling frequency, this
is an important advantage of our numerical approach.