<s>
The	O
trinomial	B-Application
tree	I-Application
is	O
a	O
lattice-based	B-Application
computational	B-Application
model	I-Application
used	O
in	O
financial	O
mathematics	O
to	O
price	O
options	O
.	O
</s>
<s>
It	O
is	O
an	O
extension	O
of	O
the	O
binomial	B-Application
options	I-Application
pricing	I-Application
model	I-Application
,	O
and	O
is	O
conceptually	O
similar	O
.	O
</s>
<s>
For	O
fixed	O
income	O
and	O
interest	O
rate	O
derivatives	O
see	O
Lattice	B-Application
model	I-Application
(	O
finance	O
)	O
#Interest	O
rate	O
derivatives	O
.	O
</s>
<s>
As	O
with	O
the	O
binomial	O
model	B-Application
,	O
these	O
factors	O
and	O
probabilities	O
are	O
specified	O
so	O
as	O
to	O
ensure	O
that	O
the	O
price	O
of	O
the	O
underlying	O
evolves	O
as	O
a	O
martingale	O
,	O
while	O
the	O
moments	O
considering	O
node	O
spacing	O
and	O
probabilities	O
are	O
matched	O
to	O
those	O
of	O
the	O
log-normal	O
distribution	O
(	O
and	O
with	O
increasing	O
accuracy	O
for	O
smaller	O
time-steps	O
)	O
.	O
</s>
<s>
Once	O
the	O
tree	O
of	O
prices	O
has	O
been	O
calculated	O
,	O
the	O
option	O
price	O
is	O
found	O
at	O
each	O
node	O
largely	O
as	O
for	O
the	O
binomial	O
model	B-Application
,	O
by	O
working	O
backwards	O
from	O
the	O
final	O
nodes	O
to	O
the	O
present	O
node	O
(	O
)	O
.	O
</s>
<s>
The	O
resulting	O
model	B-Application
is	O
soluble	O
and	O
there	O
exist	O
analytic	O
pricing	O
and	O
hedging	O
formulae	O
for	O
various	O
options	O
.	O
</s>
<s>
The	O
trinomial	O
model	B-Application
is	O
considered	O
to	O
produce	O
more	O
accurate	O
results	O
than	O
the	O
binomial	O
model	B-Application
when	O
fewer	O
time	O
steps	O
are	O
modelled	O
,	O
and	O
is	O
therefore	O
used	O
when	O
computational	O
speed	O
or	O
resources	O
may	O
be	O
an	O
issue	O
.	O
</s>
<s>
For	O
vanilla	O
options	O
,	O
as	O
the	O
number	O
of	O
steps	O
increases	O
,	O
the	O
results	O
rapidly	O
converge	O
,	O
and	O
the	O
binomial	O
model	B-Application
is	O
then	O
preferred	O
due	O
to	O
its	O
simpler	O
implementation	O
.	O
</s>
<s>
For	O
exotic	O
options	O
the	O
trinomial	O
model	B-Application
(	O
or	O
adaptations	O
)	O
is	O
sometimes	O
more	O
stable	O
and	O
accurate	O
,	O
regardless	O
of	O
step-size	O
.	O
</s>
