Multi
Period
Binomial
Model

Secondary
Market
Now
we
are
going
to
add
one
contingent
claim
(derivative)
to
the
multi
period
binomial
Market.
In
this
section,
we
start
by
adding
a
European
contingent
claim
StockBondContingent
Claim
Market
Consider
a
financial
market
in
which,
in
addition
to
stock
and
bond,
there
is
one
European
contingent
claim
that
can
be
traded.
®
(:
Price
of
the
contingent
claim
at
time
t
=
0
e
T:expiration
time
of
the
contingent
claim
e
X:
The
final
value
of
the
contingent
claim
at
the
expiratointimet
=T
¢
Ingeneral,
X
can
depend
on
the
stock
price
during
the
whole
interval
t
=
0,1,2,..,T
(and
not
only
the
final
stock
price
St)
X
=
F(So,
51,
52,
,ST)
Example
1.
If
X
is
a
European
call
option
with
expiration
time
T
and
strike
price
K:
T
.
X
=
(Sr

KB
P
S?C—OQ'
G'
)(
Qv\\a
ée?tué\
an
S.'.
Example
2.
If
X
is
a
European
put
option
with
expiration
time
T
and
strike
price
K:
X:
(,k'
S'T
\*
3?'—0&'
G'
)(
Qw\a
éd»]mé\
an
S.\.
Example
3.
We
can
potentially
consider
a
European
contingent
claim
with
expiration
time
T=4
whose
final
value
is
defined
by
X
=
Max(S3,S4)
Example
4.
Consider
a
binomial
model
with
S
=
4,d
=
0.5,u
=
3,r
=
0.5.
Let
X
be
a
European
contingent
claim
with
expiration
time
T=2.
For
the
following
cases,
find
all
possible
final
values
of
X.
.k
(a)
X
is
a
European
call
option
with
strike
price
K=5.
X:
KSJ__":)\
X
__w\fiX(Sq,'al
4")
(b)
X
=
Max
(Sg,
S1,
S2)
o
PRI,
SRV
KT
RV
SRUIe!
(R
§
NS
Pt
¥
s
L3N

\
\
Sy

w88z
by
(hn)L
()
__Mx(h,n,L)_
n
SQ=L('
S
14y
6
'
RN
17
SXD)
=
£
1ea)
s\
(Ue)
=mere(
§,
L8
=
\s.."%'L
A

e
=
_
\
.

Lx;'—
\
Xs(\:S)'Fo
{(uj\a"'"'""'"l"\fq'