RUTCOR Brown Bag
RUTCOR Lounge
Andras Prekopa
RUTCOR -
On the analytical-numerical
valuation of the Bermudan and American Options
Abstract: The paper further develops, both from the theoretical and numerical
points of view the analytic valuation of the American options, initiated by Geske and Johnson (1984) for the American put with no
dividend. We present and prove closed form formulas for the Bermudan put and
call, with dividend, paid continuously at a constant rate, where a general
number and not necessarily equal length intervals subdivide the time. Based on
the obtained formulas and recent, efficient numerical integration techniques,
to obtain values of the multivariate normal c.d.f.,
the Bermudan put and call option values are evaluated
for up to twenty subdividing intervals. The sequences of option values are smoothed by sums of exponential functions and the latters are used to predict the values of the American
options. Numerical results are presented and compared with
those, published in the literature. It is shown
that the binomial method systematically overestimates the option price and so
do other methods we have looked at, according to our results. Some properties
of