Pricing Parisian Style Options with a Lattice Method
Marco Avellaneda and Lixin Wu
IJTAF 1999
A Parisian-style barrier option expires
worthless if the price of the underlying asset remains above
or below some level(s) continuously over a specified period of time (the
``window''). A trinomial-lattice scheme is developed for calculating the
price and the sensitivities of such options. Monte Carlo simulation
of hedging events using the resulting deltas show errors which are
of the same order-of-magnitude as those found when hedging plain-vanilla
options, confirming the validity of the proposed scheme. We use these results
to price callable and convertible bonds with the ``window'' feature.