Mathematical Finance Seminar
October 26, 2000 , 5:30 PM to 7:00 PM
Tse Leung Lai, Stanford University
Valuation and exercise boundaries of American barrier and lookback options
We first present a relatively simple method for the numerical solution
of
optimal stopping problems associated with American path-dependent
options,
yielding benchmark values for American barrier or lookback puts and
calls.
By decomposing an American barrier or lookback option price as the sum
of
the corresponding European option price, which has a closed-form
expression, and the early exercise premium, which can be expressed as an
integral whose integrand is an explicit function of the exercise
boundary,
we develop fast and accurate approximations to the option prices and
hedge
parameters.