Financial Market
Derivatives Market – Vanilla Options – Call option
Financial Market
Derivatives Market – Vanilla Options – Call option
HOLDER
WRITER
Participans:
The deal:
For a specific period of time
HOLDER
will have a
RIGHT to buy
some underling security for a price specified today.
Options’ features:
when the maturity comes, holder has the right
to demand from option’s writer to sell him particular security at price specified in contract.
WRITER
will have an
OBLIGATION
to deliver
the underlying security.
Strike (Exercise price) (K) = price at which the underlying transaction will occur upon exercise.
Expiration date (Maturity) (T) = the day when the options expiry.
Multiplier (N) = the quantity of the underlying asset.
Underlying security = what security is going to be traded.
CALL option
= holder gets the
right to buy
=
Financial Market
Derivatives Market – Vanilla Options – Call option
Today
Maturity
Holder
gets
the right
for a
future transaction.
Holder can
(but doesn’t have to)
finalize
transaction.
Example 1:
A is signing a contract with B specifying that in a one year from now he will have the right to
buy 1 stock of X company for a 10$ (the price specified in the contract).
Today
After 1 year
A
gets the
right
to buying 1 stock of
X company from
B
but after 1 year.
A can
buy 1 stock of X company.
B must
sell that 1 stock, if
A
will call for that.
Writer is obliged
to finalize transaction
but
only if holder calls
for that.
Financial Market
Derivatives Market – Vanilla Options – Call option
Data from example 1:
Will CALL
’s holder execute his rights ??
Underlying security = Stock X
N = 1
T = 1 year
K = 10 $
Let’s assume that stock X price after T is going to be:
a) S
T
= 20 $
b) S
T
= 15 $
e) S
T
= 10 $
c) S
T
= 8 $
d) S
T
= 5 $
CALL
’s holder has the right to buy stock X for 10 $ (stock X is listed with higher
price at this moment)
– Holder executes his right and in the same moment
sells stock X at the market for a higher price.
CALL
’s holder will not execute his right while he can buy the same stock at the
market much cheaper. Hence CALL option is worthless.
CALL
’s holder will not execute his right while he can buy the same stock at the
market at the same price. Hence CALL option is worthless.
Financial Market
Derivatives Market – Vanilla Options – Call option
CALL
option
HOLDER
will execute his right when:
S
T
> K
What will be CALL
’s holder payoff (if Strike = 10 $):
a) S
T
= 20 $
b) S
T
= 15 $
e) S
T
= 10 $
c) S
T
= 8 $
d) S
T
= 5 $
CALL
’s holder executes his right: he buys stock X for 10 $ from writer.
At the same moment, he sells this security for:
a) 20 $ b) 15 $
a) 10 $
b) 5 $
Payoff:
CALL’s holder will not execute his right, while he can buy the same stock from
market for:
c) 8 $ d) 5 $
c) 0 $
d) 0 $
Payoff:
CALL’s holder will not execute his right, while he can buy the same stock from
market for the same price.
e) 0 $
Payoff:
Financial Market
Derivatives Market – Vanilla Options – Call option
CALL’s
holder
payoff function:
K
0
S
T
Payoff
In general:
10 $
0
S
T
Payoff
Data from example 1 (K = 10 $):
15 $
20 $
5 $
5 $
10 $
MAX(S
T
– K , 0)
Payoff function for CALL’s
holder
=
Financial Market
Derivatives Market – Vanilla Options – Call option
Data form example 1:
CALL’s
writer
payoff function:
a) S
T
= 20 $
b) S
T
= 15 $
e) S
T
= 10 $
c) S
T
= 8 $
d) S
T
= 5 $
Writer will be asked by the holder to sell the security. Hence, writer will buy
stock X from the market (paying a) 20 $ b) 15 $) and will sell this stock
immediately to holder (asking 10 $).
Writer won’t be called to sell the stock X, while holder will not execute his right.
c) 0 $
d) 0 $
e) 0 $
Payoff:
a) -10 $ b) -5 $
Payoff:
Underlying security = Stock X
N = 1
T = 1 year
K = 10 $
Let’s assume that stock X price after T is going to be:
Underlying security = Stock X
N = 1
T = 1 year
K = 10 $
Financial Market
Derivatives Market – Vanilla Options – Call option
K
0
S
T
Payoff
10 $
0
S
T
Payoff
15 $
20 $
5 $
- 5 $
- 10 $
- MAX(S
T
– K , 0)
CALL’s
writer
payoff function:
In general:
Data from example 1 (K = 10 $):
Payoff function for CALL’s
writer
=
Financial Market
Derivatives Market – Vanilla Options – Call option
Holder
Writer
K
0
S
T
Payoff
K
0
S
T
Payoff
HOLDER
WRITER
Holder:
has
nothing to lose
– can
make a big profit.
This is why
when the contract is signed
writer
demands a
single payment
(
Premium
)
from
holder
for giving him the right to buy some security in
the future for a price specified today.
This is definitely unfair.
c
–
CALL
option price
(Premium, which needs to be paid by the holder to the
writer for obtaining the right for a future transaction).
Writer:
he is
risking a lot
- got
nothing to gain.
Financial Market
Derivatives Market – Vanilla Options – Call option
What will be
CALL’s
holder profit
(K = 10 $, c = 5 $) assuming that the stock X price is going to be:
a) S
T
= 20 $
b) S
T
= 15 $
e) S
T
= 10 $
c) S
T
= 8 $
d) S
T
= 5 $
CALL’s holder executes his right an gain: a) 10 $ b) 5 $. Unfortunately, he has
paid a 5 $ premium to a writer, hence the final profit is going to be:
a) 5 $
b) 0 $
Profit:
CALL option is worthless, but holder has paid 5 $ premium, hence the profit is:
c) - 5 $
d) - 5 $
Profit:
e) - 5 $
Profit:
Holder’s
payoff - premium =
Holder’s
profit
CALL option is worthless, but holder has paid 5 $ premium, hence the profit is:
Financial Market
Derivatives Market – Vanilla Options – Call option
Payoff function Profit function
for CALL’s
holder
:
10 $
0
S
T
Payoff
Payoff function (K = 10 $):
15 $
20 $
5 $
5 $
10 $
10 $
0
S
T
Profit
15 $
20 $
5 $
5 $
Profit function (K = 10 $, c = 5 $):
- 5 $
10 $
- 5 $
Financial Market
Derivatives Market – Vanilla Options – Call option
Payoff function
and
Profit function
for CALL’s
holder:
0
S
T
K
- c
- c
- c
- c
- c
- c
K + c
$
Financial Market
Derivatives Market – Vanilla Options – Call option
MAX(S
T
– K , 0) - c
Profit
function for CALL’s
holder
=
a) S
T
= 20 $
b) S
T
= 15 $
e) S
T
= 10 $
c) S
T
= 8 $
d) S
T
= 5 $
Writer will be asked to sell stock X, hence writer will make: a) - 10 $ b) - 5 $.
On the other hand writer gain 5 $ premium for writing the contract. To sum it up,
writer’s profit is equal to:
a) - 5 $
b) 0 $
Profit:
CALL
option is worthless. Writer’s will be left with a premium:
c) 5 $
d) 5 $
Profit:
e) 5 $
Profit:
Writer
’s
payoff + premium =
Writer’s
profit
What will be
CALL’s
writer profit
(K = 10 $, c = 5 $) assuming that the stock X price is going to be:
CALL
option is worthless. Writer’s will be left with a premium:
Financial Market
Derivatives Market – Vanilla Options – Call option
10 $
0
S
T
15 $
20 $
5 $
- 5 $
- 10 $
10 $
0
S
T
15 $
5 $
- 5 $
- 10 $
5 $
5 $
20 $
Payoff function Profit function
for CALL’s
writer:
Payoff
Payoff function (K = 10 $):
Profit
Profit function (K = 10 $, c = 5 $):
Financial Market
Derivatives Market – Vanilla Options – Call option
0
S
T
$
K
c
K + c
Payoff function
Profit function
+ c
+ c
+ c
+ c
Payoff function
and
Profit function
for CALL’s
writer:
Financial Market
Derivatives Market – Vanilla Options – Call option
- MAX(S
T
– K , 0) + c
Profit
function for CALL’s
writer
=
Payoff and Profit Functions
for CALL’s
holder
and
writer
S
T
Payoff
S
T
Payoff
S
T
Profit
S
T
Profit
H
O
L
D
E
R
W
R
I
T
E
R
Financial Market
Derivatives Market – Vanilla Options – Call option
CALL Premium (c)
Option premium
Intrinsic value
Time Value
+
=
What will be an option payoff if it
would expire right now.
Max ( S
0
– K ; 0 )
What could happen in a future.
c – Max ( S
0
– K ; 0 )
Time value
approaches
zero
as the expiration date nears.
Financial Market
Derivatives Market – Vanilla Options – Call option
CALL Premium (c)
CALL option premium mostly depends on:
S
0
– spot price (what is the current underlying security price).
K
– Strike (execution price).
T
– Time (How long this option is going to live).
When the other variables are constant then:
If
S
0
raises
then
If
S
0
falls
then
If
T raises
then
If
T falls
then
If
K raises
then
If
K falls
then
c raises too
.
c falls.
c raises too
.
c falls too
.
c raises
.
c falls too
.
Financial Market
Derivatives Market – Vanilla Options – Call option
Terminology:
Based on relationship between S
0
and K we can distinguish such options:
IN the money
(ITM)
AT the money
(ATM)
OUT of the money
(OTM)
K
0
S
0
Payoff
CALL option is:
ITM
when S
0
>
K
ATM
when S
0
=
K
OTM
when S
0
<
K
ITM
ATM
OTM
Financial Market
Derivatives Market – Vanilla Options – Call option