<s>
In	O
mathematical	O
finance	O
,	O
a	O
Monte	B-Algorithm
Carlo	I-Algorithm
option	I-Algorithm
model	I-Algorithm
uses	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
to	O
calculate	O
the	O
value	O
of	O
an	O
option	O
with	O
multiple	O
sources	O
of	O
uncertainty	O
or	O
with	O
complicated	O
features	O
.	O
</s>
<s>
An	O
important	O
development	O
was	O
the	O
introduction	O
in	O
1996	O
by	O
Carriere	O
of	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
for	O
options	O
with	O
early	O
exercise	O
features	O
.	O
</s>
<s>
In	O
terms	O
of	O
theory	O
,	O
Monte	B-Algorithm
Carlo	I-Algorithm
valuation	I-Algorithm
relies	O
on	O
risk	O
neutral	O
valuation	O
.	O
</s>
<s>
Here	O
the	O
price	O
of	O
the	O
underlying	O
instrument	O
is	O
usually	O
modelled	O
such	O
that	O
it	O
follows	O
a	O
geometric	B-Language
Brownian	I-Language
motion	I-Language
with	O
constant	O
drift	O
and	O
volatility	O
.	O
</s>
<s>
Since	O
the	O
underlying	O
random	O
process	O
is	O
the	O
same	O
,	O
for	O
enough	O
price	O
paths	O
,	O
the	O
value	O
of	O
a	O
european	O
option	O
here	O
should	O
be	O
the	B-Algorithm
same	I-Algorithm
as	I-Algorithm
under	I-Algorithm
Black	I-Algorithm
–	I-Algorithm
Scholes	I-Algorithm
.	O
</s>
<s>
Here	O
,	O
for	O
each	O
randomly	O
generated	O
yield	B-Algorithm
curve	I-Algorithm
we	O
observe	O
a	O
different	O
resultant	O
bond	O
price	O
on	O
the	O
option	O
's	O
exercise	O
date	O
;	O
this	O
bond	O
price	O
is	O
then	O
the	O
input	O
for	O
the	O
determination	O
of	O
the	O
option	O
's	O
payoff	O
.	O
</s>
<s>
(	O
Whereas	O
these	O
options	O
are	O
more	O
commonly	O
valued	O
using	O
lattice	B-Application
based	I-Application
models	I-Application
,	O
as	O
above	O
,	O
for	O
path	O
dependent	O
interest	O
rate	O
derivatives	O
–	O
such	O
as	O
CMOs	O
–	O
simulation	O
is	O
the	O
primary	O
technique	O
employed	O
.	O
)	O
</s>
<s>
To	O
apply	O
simulation	O
to	O
IRDs	O
,	O
the	O
analyst	O
must	O
first	O
"	O
calibrate	O
"	O
the	O
model	O
parameters	O
,	O
such	O
that	O
bond	O
prices	O
produced	O
by	O
the	O
model	O
best	B-Algorithm
fit	I-Algorithm
observed	O
market	O
prices	O
.	O
</s>
<s>
Monte	B-Algorithm
Carlo	I-Algorithm
Methods	I-Algorithm
allow	O
for	O
a	O
compounding	O
in	O
the	O
uncertainty	O
.	O
</s>
<s>
As	O
required	O
,	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulation	I-Algorithm
can	O
be	O
used	O
with	O
any	O
type	O
of	O
probability	O
distribution	O
,	O
including	O
changing	O
distributions	O
:	O
the	O
modeller	O
is	O
not	O
limited	O
to	O
normal	O
or	O
log-normal	O
returns	O
;	O
see	O
for	O
example	O
Datar	O
–	O
Mathews	O
method	O
for	O
real	O
option	O
valuation	O
.	O
</s>
<s>
The	O
value	O
is	O
defined	O
as	O
the	O
least	B-Algorithm
squares	I-Algorithm
regression	I-Algorithm
against	O
market	O
price	O
of	O
the	O
option	O
value	O
at	O
that	O
state	O
and	O
time	O
(	O
-step	O
)	O
.	O
</s>
<s>
As	O
can	O
be	O
seen	O
,	O
Monte	B-Algorithm
Carlo	I-Algorithm
Methods	I-Algorithm
are	O
particularly	O
useful	O
in	O
the	O
valuation	O
of	O
options	O
with	O
multiple	O
sources	O
of	O
uncertainty	O
or	O
with	O
complicated	O
features	O
,	O
which	O
would	O
make	O
them	O
difficult	O
to	O
value	O
through	O
a	O
straightforward	O
Black	O
–	O
Scholes-style	O
or	O
lattice	B-Application
based	I-Application
computation	O
.	O
</s>
<s>
Conversely	O
,	O
however	O
,	O
if	O
an	O
analytical	O
technique	O
for	O
valuing	O
the	O
option	O
exists	O
—	O
or	O
even	O
a	O
numeric	B-General_Concept
technique	I-General_Concept
,	O
such	O
as	O
a	O
(	O
modified	O
)	O
pricing	B-Application
tree	I-Application
—	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
will	O
usually	O
be	O
too	O
slow	O
to	O
be	O
competitive	O
.	O
</s>
<s>
They	O
are	O
,	O
in	O
a	O
sense	O
,	O
a	O
method	O
of	O
last	O
resort	O
;	O
see	O
further	O
under	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
in	I-Algorithm
finance	I-Algorithm
.	O
</s>
