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From: r_poetic on 18 Mar 2010 11:28
Greetings,
I am formulating a model for the rate at which certain options are
exercised. These options can be exercised on the first of the option
year, up to a specified time limit. E.g., if the option is effective
on Jan 5, 2011 with a 10 year limit, then it can be exercised on Jan
5, 2012, Jan 5, 2013, ... jan 5, 2020, after which it would exire if
not exercised. The data include about 3000 observations. Looking at a
histogram, overall there is a fairly steady exercise rate of about 90%
of the remaining options each year, so I initially think that a
negative binomial regression would be appropriate. However, the first
and last year are somewhat different. The first year has a smaller
exercise rate overall; it is very unlikely the people have cause to
exercise the option so soon after buying it. And the last year has a
larger exercise rate, because people realize that, roughly speaking,
it's now or never. It seems that the probability of the neg binomial,
which is constant p, is p+delta for the first year and p-epsilon in
the last year. I am trying to retain the simplicity of the neg
binomial, instead of a time series model with a different exercise
rate for each year. What is the best approach to take?
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