Derivative
Securities
Individual
REQUIREMENTS:
1.
Answer
all
questions.
2. You
need
to provide
a
detailed,
clearly-arranged
solution
for
all
questions.
Providing
merely
a
number
as
a
result
without
showing
how
you
have
obtained
this
result
will
lead
to 0 marks
for
the
corresponding
question.
Using
tables
and
diagrams
may
be
very
helpful
for
providing
clearly-arranged
solutions.
3.
All answers
must
be
of
proper
English
expression
and
grammar.
Derivative
Securities
Problem1:Properties
ofOptions(4
marks)
Consider
a
four-month
European
call
option
on a
dividend-paying
stock.
The
stock
price
is
$75,
the
strike
price
is
$70,
and
a
dividend
of
$1.50
is expected
in
three
months.
The
risk-free
interest
rate
is
8%
per
annum
for
all
maturities.
a.
What
is
the lower
bound
for
the
price
of
this call?
b.
Assume that
the
call
is
currently
selling
for
$3.
Describe
in
detail
with
which strategy
you
can
gain
an
arbitrage
profit
and
how much
this
profit
will
be.
Problem2:Properties
ofOptions
(6
marks)
The
price
of
a
European
call
that
expires
in six
months
and
has
a strike
price
of
$50
is $5. The
underlying
stock
price
is
$52,
and
a
dividend
of
$1.00
is expected
in three
months.
The
term
structure
is
flat, with all risk-free
interest
rates
being
10%.
a.
What
is
the price
of
a
European
put option
on
the
same
stock that expires
in six
months
and
has
a strike
price
of
$50?
b.
Explain
in
detail
the
arbitrage
opportunities
if the
European
put price
is
$0.50.
How
much
will
be
the
arbitrage
profit?
Problem
3: BinomialTrees(5marks)
A
stock
price
is
currently
$30.
Over
each
of the
next
two
three-month
periods
it
is
expected
to go
up
by
8%
or
down
by
10%.
The
risk-free
interest
rate
is
5%
per
annum
with
continuous
compounding.
a.
Use
a
two-step
binomial
tree
to
calculate
the
value
of
a
six-month
European
put option
with a strike
price
of
$32.
b.
Use
a
two-step
binomial
tree
to
calculate
the
value
of
a six-month
American
put option
with a strike
price
of
$32.
c.
Use
a
two-step
binomial
tree
to
calculate
the
value
of
a
six-month
European
call
option
with a strike
price
of
$32.
d.
Show
whether
the
put-call-parity
holds
for
the
European
put and the
European
call.
e.
Calculate
the deltas
of the
European
put and the
European
call
at
the
different
nodes of
the
binomial
three.
Hint:
You need
to calculate
three
deltas
for
the
call
and
three
deltas
for
the
put.
Problem
4: BinomialTrees(5marks)
A
stock
price
is
currently
$40.
During
each
two-month
period
for
the
next
four
months it
is
expected
to increaseby10%or
decrease
by8%.
The
risk–freeinterest
rate
is
5%. Useatwo–step
tree
to
calculate
the
value
of
a derivative
that
pays
off
(max[(ST-35),0])2where
pricein
fourmonths.
ST
is
the stock
a.
Use
no-arbitrage
arguments
(you
need
to show how
to set
up the
riskless
portfolios at the different
nodes
of the
binomial
tree).
b.
Use
risk-neutral
valuation.
c.
Verify
whether
both
approaches
lead
to
the
same
result.
d.
If
the
derivative
is
of
American
style,
should it be
exercised
early?
(continues
on
nextpage)
Problem
5. Valuing
StockOptions:TheBlack–Scholes-MertonModel(10marks)
This
is
aBloomberg–basedexercise.
Beforemaking
anycalculations,
pleasedo
the following:
Go
to the Trading
Room
and
login
in
Bloomberg
(G42
2.16 at
Gold Coast
Campus
and
N50 0.32E
at
Nathan
Campus).
You can
find the
Trading
Room
timetable
in
the
folder
“Bloomberg
Activities”
under
“Course
Content”
on
L@G.
In
the same
folder,
you
can
also
find materials
which
will
be
useful
for
your
work
with Bloomberg.
Search
for
the
share
of
Google
(Bloomberg
ticker:
GOOGL).
Download
daily
price
data
for
the
Google
share
price
over
the
last
250 trading
days.
Go
to the
Options
Monitor
showing
option
contracts
on
the Google
share
(Use
OMON
<Go>
).
Find
the
put
and the
call
options
with
o
Expiration
in October
2017
and
o
Strike
price
$940
Make
screenshot(s)
showing
the
prices
of these
options.
Hint:You
can
make
screenshots
and
email
them
to
yourself
via
GRAB
<Go>.
Use
LR
<Go>
to
obtain
a
LIBOR
value
for
the same
day
as
the option price
data.
Choose
the USD
LIBOR
with time
horizon
closest
to
the time-to-maturity
of
the
options.
Document
with a screenshot.
Once
you
have
this
data,
you
can
start
with the
calculations:
(a)
Calculate
with
Excel
the
daily
returns
of
the
Google
share
and
calculate
afterwards
their
standard
deviation
over
the
last
250 days.
(b)
Convert
the daily
volatility
to
volatility
per
annum.
(c)
Use
the
Black-Scholes-Merton
pricing
formulas
for
European
options
and
calculate
the theoretical
prices
of a
European
call
and
a
European
put
option
with
expiration
in October
2017
and
strike
price
of
$940
on
the Google
share.
Use
the
LIBOR
rate
you
have
downloaded
as
a
proxy
of
the
risk-free
rate.
(d)
Insert
the
Black-Scholes-Merton
prices
you
just calculated
in the put-call-parity.
Does
it hold?
(e)
How
would
the result
of
(c)
change
if
a
dividend
of
$2
is expected
in four
months?
(f)
Compare
the
Black-Scholes-Merton
prices
you
calculated
in
(c)
with
the
prices
of these
options
given
in Bloomberg
(use
the
average
of
bid and
ask
price
as
the
Bloomberg
price).
Are
there
any
deviations
between
the theoretical
prices
you
have
calculated
and
the prices
given
in
Bloomberg?
If
yes,
what
could be
possible
reasons
for
these
deviations?
Hint:There
are
no
dividends
announced
for
August,
September
and
October
2017.
Additional
submissionrequirements
forproblem5:
Additionally
to
your
calculations,
please
insert
in
the
Word
file that
you
will
submit
the
screenshots
you
have
made
showing
the
spot
price,
option
prices
and
LIBOR
which
you
used.
Upload
the Excel
file
showing
the
calculation
of
the
standard
deviation
in
(a).
ENDOFASSIGNMENT
The post Derivative Securities Individual appeared first on My Assignment Online.