Options Markets
1
Specification of
Exchange-Traded Options
Expiration date
Strike price
European or American
Call or Put (option class)
2
Terminology
Moneyness :
At-the-money option
Would lead to zero cash flow if exercised immediately
Near-the-money
In-the-money option
Would lead to positive cash flow if exercised
immediately
Out-of-the-money option
Would lead to negative cash flow if exercised
immediately
3
Terminology
Option class
Options of the same type (Call or Put)
Option series
Options of a given class with same expiration date
and strike price
Intrinsic value
Maximum of zero and the value if exercised
immediately.
Time value
4
Options Example
ABC stock is trading at Rs. 2,751 on Jul 15, and
the most traded options expiring on Jul 31 on
the stock are selling at:
Option Strike
Call
2,740
Call
2,760
Call
2,780
Put
2,700
Put
2,740
Premium
26.6
17.7
12.5
7.9
18
Calculate intrinsic value and time value.
5
Options Example
SYMBOL
EXPIRY
DATE
RELIANCE
29-Aug-24
RELIANCE
29-Aug-24
RELIANCE
29-Aug-24
HDFCBANK
29-Aug-24
HDFCBANK
29-Aug-24
TATAMOTORS 29-Aug-24
HDFCBANK
29-Aug-24
TATAMOTORS 29-Aug-24
RELIANCE
29-Aug-24
BAJFINANCE 29-Aug-24
AXISBANK
29-Aug-24
LT
29-Aug-24
ITC
29-Aug-24
INFY
29-Aug-24
ADANIENT
29-Aug-24
LT
29-Aug-24
INFY
29-Aug-24
TATAMOTORS 29-Aug-24
TCS
29-Aug-24
ICICIBANK
29-Aug-24
SBIN
29-Aug-24
TATAPOWER 29-Aug-24
OPTION STRIKE
TYPE
PRICE
Call
Put
Call
Call
Put
Call
Call
Put
Put
Call
Call
Call
Call
Call
Put
Call
Put
Put
Put
Call
Put
Call
3000
3000
3100
1650
1600
1100
1600
1000
2900
7000
1200
3700
500
1900
3000
3800
1800
1100
4300
1200
840
450
LTP
80.15
52.1
38.5
23
22
48
47.1
5.6
20.35
108
22.55
105.65
17.4
34.35
62.05
61
13.75
27.3
41.65
41.7
16.55
14.2
OPEN
%CHNG VOLUME
VALUE
INTEREST STOCK
(Contracts) (₹ Lakhs) (Contracts) PRICE
20.44
30,421
5,901.67
13,518
3,018.60
-31.22
13,158
1,863.17
10,206
3,018.60
23
18,025
1,674.52
9,333
3,018.60
-8.73
16,211
1,985.60
8,775
1,616.30
-1.35
13,121
1,823.62
6,858
1,616.30
30.26
28,067
6,200.98
6,351
1,116.05
-7.37
16,385
4,094.04
5,923
1,616.30
-32.53
8,398
327.02
5,333
1,116.05
-41.61
7,150
413.45
5,318
3,018.60
38.64
13,883
1,669.08
5,242
6,799.50
-1.74
16,313
2,193.08
4,494
1,176.00
42.19
16,125
2,078.19
4,021
3,699.00
53.98
16,800
4,134.14
3,882
501.55
85.68
20,361
2,553.27
3,865
1,880.00
-41.82
8,048
1,658.45
3,829
3,072.25
42.03
13,659
978.94
3,330
3,699.00
-51.41
9,920
659.08
3,304
1,880.00
-32.68
10,173
1,915.22
3,175
1,116.05
-42.59
9,199
776.26
3,034
4,393.65
25.98
16,322
4,003.46
2,969
1,217.00
-20.81
6,955
938.93
2,936
859.95
91.89
17,514
3,120.99
2,914
445
6
Dividends & Stock Splits
Suppose you own N options with a strike
price of X :
No adjustments are made to the option terms for
cash dividends
When there is an n-for-m stock split,
the strike price is reduced to mX/n
the no. of options is increased to nN/m
Stock dividends are handled in a manner similar
to stock splits
7
Dividends & Stock Splits
(continued)
Consider a call option to buy 100
shares for $20/share
How should terms be adjusted:
for a 2-for-1 stock split?
for a 5% stock dividend?
8
Warrants
Warrants are options that are issued (or written)
by a corporation or a financial institution
The number of warrants outstanding is
determined by the size of the original issue &
changes only when they are exercised or when
they expire
9
Warrants (continued)
Warrants are traded in the same way as stocks
The issuer settles up with the holder when a
warrant is exercised
When call warrants are issued by a corporation
on its own stock, exercise will lead to new
treasury stock being issued
10
Executive Stock Options
Option issued by a company to executives
When the option is exercised the company
issues more stock
Usually at-the-money when issued
11
Executive Stock Options
continued
They become vested after a period ot time
They cannot be sold
They often last for as long as 10 or 15 years
12
Convertible Bonds
Convertible bonds are regular bonds that
can be exchanged for equity at certain times
in the future according to a predetermined
exchange ratio
Very often a convertible is callable
The call provision is a way in which the
issuer can force conversion at a time earlier
than the holder might otherwise choose
13
Margins
Margins are required when options are sold
When a naked option is written the margin is the
greater of:
A total of 100% of the proceeds of the sale plus 20%
of the underlying share price less the amount (if any)
by which the option is out of the money
A total of 100% of the proceeds of the sale plus 10%
of the underlying share price
India, SPAN margin plus Exposure margin, and
premium not available for use
For other trading strategies there are special rules
14
Properties of
Stock Option Prices
15
Notation
c : European call
option price
p : European put
option price
S0 : Stock price today
X : Strike price
T : Life of option
: Volatility of stock
price
C : American Call
option price
P : American Put option
price
ST :Stock price at time T
D : Present value of
dividends during option’s
life
r : Risk-free rate for
maturity T with cont comp
16
Effect of Variables on Option
Pricing
Variable
c
S0
X
T
r
D
+
–
?
+
+
–
p
–
+?
+
–
+
C
+
–
+
+
+
–
P
–
+
+
+
–
+
17
American vs European Options
An American option is worth
at least as much as the
corresponding European
option
C c
P p
18
Calls: An Arbitrage Opportunity?
Suppose that
c =3
T =1
X = 18
S0 = 20
r = 10%
D=0
Is there an arbitrage opportunity?
19
Lower Bound for European Call Option
Prices; No Dividends
c S0
–rT
-Xe
20
Puts: An Arbitrage Opportunity?
Suppose that
p =1
T = 0.5
X = 40
S0 = 37
r = 5%
D =0
Is there an arbitrage opportunity?
21
Lower Bound for European Put
Prices; No Dividends
-rT
p Xe - S0
22
Put-Call Parity; No Dividends
Consider the following 2 portfolios:
Portfolio A: European call on a stock + PV of the
strike price in cash
Portfolio B: European put on the stock + the stock
Both are worth MAX(ST , X ) at the maturity of
the options
They must therefore be worth the same today
This means that
c + Xe -rT = p
+ S0
23
Put-Call Parity: Another Way
Fiduciary Call: Long European call and a riskfree bond. The bond matures on the option
expiration day and has a face value equal to the
exercise price of the call.
Protective Put: Long European put and long
underlying asset
24
Combination of Packages of Puts and
Calls
Transaction
Fiduciary Call
Buy Call
Buy bond
Total
Protective Put
Buy Put
Buy underlying asset
Total
Current Value
Value at Expiration
ST X
ST X
c
Xe-rT
c + Xe-rT
0
X
X
ST - X
X
ST
p
S0
p + S0
X - ST
ST
X
0
ST
ST
25
Put-Call Parity: Another Way
Thus, the Fiduciary Call and the Protective Put
end up with the same value, and hence they are
identical combinations. To avoid arbitrage,
their values today must be the same.
Thus,
c + Xe-rT = p + S0
This is the put-call parity relationship
26
Synthetic Call and Put
Rearranging, we get
c = p + S0 - Xe-rT
This is known as a synthetic call position, as the
combination of long put, long asset and
borrowing risk-free bond is equivalent to a call
position.
Similarly,
p = c - S0 + Xe-rT
This is a synthetic put position created by long
call, short asset and long bond.
27
Call and Synthetic Call
Transaction
Call
Buy Call
Synthetic Call
Buy Put
Buy underlying asset
Issue Bond
Total
Current Value
Value at Expiration
ST X
ST X
c
0
ST - X
p
S0
-Xe-rT
p + S0 - Xe-rT
X - ST
ST
-X
0
0
ST
-X
ST - X
28
Put and Synthetic Put
Transaction
Current Value
Put
Buy Put
p
Synthetic Put
Buy Call
c
Short underlying asset
-S0
Issue Bond
Xe-rT
Total
c - S0 + Xe-rT
Value at Expiration
ST X
ST X
X - ST
0
0
-ST
X
X - ST
ST - X
-ST
X
0
29
Synthetic Call and Put
Similar fashion, we can create Synthetic
underlying and Synthetic bond positions.
Synthetic underlying = Long Call + Long bond
+ Short put
Synthetic bond = Long put + long underlying
+ Short call
30
Arbitrage Opportunities
Suppose that
c =3
S0 = 31
T = 0.25
r = 10%
X =30
D =0
What are the arbitrage possibilities when
p = 2.25 ?
p =1?
31
0
