In contrast to binomial processes, a trinomial process
allows a quantity to stay constant within a given period of time.
In the latter case, the increments are described by:
and the process
is again given by:
where
are mutually independent. To solve
the Black-Scholes equation, some algorithms use trinomial schemes
with time and state dependent probabilities
,
and
.
Figure 4.5 shows five simulated paths of a trinomial
process with
and
Fig.:
Five paths of a trinomial process with
(
)-intervals around the trend (which is zero) are
given as well.
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The exact distribution of
cannot be derived from the
binomial distribution but for the trinomial process a similar
relations hold:
For large
,
is approximately
N
-distributed.