CFM 306: FINANCIAL RISK MANAGEMENT
OPTION
Lecture Outline
Introduction to options
Call option
Put option
Options algebra
Practice questions
INTRODUCTION TO OPTIONS
Options are another category of derivative instruments widely used in financial markets, but they
offer a more complete form of hedging than some of the other instruments discussed earlier.
However, there is a catch: options tend to be more expensive, especially where large contracts
are concerned. The premium (price of the option) payable in accordance with a contract may be a
substantial amount, especially if there is great uncertainty or if the underlying asset is perceived
volatile (subject to many price changes). However, options offer leverage because the buyer
enjoys complete protection at a relatively low price. Once again, the contract is subject to credit
or default risk considerations when the seller of the option may not honour the agreement.
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CFM 306: FINANCIAL RISK MANAGEMENT
Note also that options can be based on various types of underlying instruments. The type of
underlying asset influences the option price. For instance, an option on foreign currency requires
six input variables as opposed to the five variables normally required. In addition to the local
risk-free interest rate, the risk-free interest rate applicable to the foreign currency must also be
entered. This affects the price of the option premium. It is therefore important to understand how
different underlying assets affect the option premium when hedges are constructed.
An option contract conveys from one party to another the right (not an obligation) to buy or sell
a specified asset at a specified price on (or before) a specified date.
There are two types of options:
a) Call option
b) Put option
Call Option
This is a financial contract which gives one party the right but not an obligation to acquire a
given number of the underlying asset in the future at a predetermined price known as the exercise
price. In this case the buyer will be required to pay the premium to the seller since the buyer will
have a right but not an obligation while the seller will be under an obligation to honour the
option contract if approached by the buyer. The value of a call option is calculated as:
The value of a call option (VC) = maximum (ST – K, 0)
Where ST = Spot market price
K= strike price or exercise price
Profit / Loss = VC – premium
-
An option is said to be in the money when, if it were exercised today, profits would be
realized.
-
An option is said to be out of the money when, if it were exercised today, losses will be
incurred.
-
An option is said to be at the money when, if it were exercised today there will be no
losses or profits (break-even point).
Options are zero sum games. This means that what the buyer gains is what the seller losses.
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CFM 306: FINANCIAL RISK MANAGEMENT
Example one
Consider a call option with the following characteristics:
-
Exercise price sh.100
-
the premium per call option sh.10
-
the time remaining to expiry of the option – 3 months
Required:
Determine the value of the call option and the profit or loss assuming the following market prices
after 3 months;
sh 80, sh 90, sh 100, sh 110, sh 120
Solution;
Mps
VC = max (ST – K, 0)
80
Max (80 -100, 0)
=0
0 – 10 = -10
90
Max (90 -100, 0)
=0
0 – 10 = -10
100
Max (100 -100, 0) = 0
0 – 10 = -10
110
Max (110 -100, 0) = 10
10 – 10 = 0
120
Max (120 -100, 0) = 20
20 – 10 = 10
Profit / Loss of buyer of call option
20
Buyer of call option/ long call
Profits
10
Option is at the money
for both buyer and seller
Option is in the
money for the seller
Option is in the
money for the buyer
0
80
Option is out of the
money for the buyer
90
100
110
120
150
Option is out of the
Price movements
money for the seller
Losses
-10
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180
Seller of call option/
short call
CFM 306: FINANCIAL RISK MANAGEMENT
For a call option; Break even point = Exercise Price + Premium
In this case, BEP = 100 + 10 = 110
2.3.1 Put Option
This is an option which gives one party the right but not an obligation to sell a specific number
of an underlying security at some future date at a predetermined price known as exercise price.
In this case since the seller is the one with the right, he will be required to pay a commitment fee
(premium) to the buyer. The value of a put option is calculated using the formula:
VP = max (K – ST, 0)
Profit / loss = VP - premium
Example two
Consider a put option with the following characteristics:Exercise price sh.50
Premium per put option sh.5
Time to expiry for the option 6 months
Calculate the value of put option and the profit or loss assuming the following market prices of
the underlying security after six months.
sh 35,sh 40 ,sh 45, sh 50, sh 60
Solution;
Mps
VP = max (K – ST, 0)
35
Max (50 - 35, 0) = 15
15– 5 = 10
40
Max (50 - 40, 0) = 10
10– 5 = 5
45
Max (50 – 45, 0) = 5
5– 5 = 0
50
Max (50 - 50, 0) = 0
0 – 5 = -5
60
Max (50 - 60, 0) = 0
0 – 5 = -5
Profit / loss of Buyer of put option
CFM 306: FINANCIAL RISK MANAGEMENT
-10
Seller of put option/ short put
Option is at the money
for both buyer and seller
Profits
-5
Option is in the
money for the seller
Option is in the
money for the buyer
-0
35
40
Option is out of the
money for the seller
45
50
60
100
Price movements
Option is out of the
money for the buyer
-5
Losses
Buyer of put option/ Long put
-10
For a put option; Break even point = Exercise Price –
Premium In this case, BEP = 50 – 5 = 45
2.3.2 Options Algebra
It is possible to determine the final payoff shape of any combination of options, including the
underlying. Options algebra is a series of + 1, 0 and – 1 values established by the number of
strikes and components of each strategy.
Each component is numbered separately with the total configuration determining the final shape.
+1
-1
0
CFM 306: FINANCIAL RISK MANAGEMENT
Each one of the strategy’s components in a strike area (before, between or after strikes) is
assigned a value depending on the direction of the line. The individual configurations are then
aggregated to arrive at the final pattern.
Example three
Consider the following data; Long 35 put, short 40 put, short 50 call and long 55 call. Establish
the options algebra final pay off pattern of this spread.
Solution;
Short 40 put
Final
Short 50 call
35
40
50
55
Long 35 put
Long 55 call
Options algebra for long 35 put;
-1
Options algebra for short 40 put;
+1
+1
0
0
Options algebra for short 50 call
0
0
0
-1
-1
Options algebra for long 55 call
0
0
0
0
+1
Final combined payoff
0
0
+1
0
0
0
-1
0
0
0
The four strikes translate to five strike areas as indicated in the diagram above.
CFM 306: FINANCIAL RISK MANAGEMENT
2.3.3 ACTIVITY TWO
Question one
Suppose that a march call option to buy a share for sh 50 costs sh 2.5 and is held until March.
Under what circumstances will the holder of the option make a profit? Under what
circumstances will the option are exercised? Draw a diagram showing how the profit on a long
position in the option depends on the stock price at the maturity of the option.
Question two
Suppose that a June put option to sell a share for sh 60 costs sh 4 and is held until June. Under
what circumstances will the seller of the option ( i.e party with the short position ) make a
profit? Under what circumstances will the option be exercised? Draw a diagram showing how
the profit from a short position in the option depends on the stock price at the maturity of the
option.
Question three
A European call and put option on shares of stock XYZ both have a strike price of Sh. 14 and
time to expiration of three months. The call option trades at Sh. 3.75 and put option at Sh. 1.50.
The risk free rate is 15% pa and the current stock price is Sh. 15. Determine the arbitrage
opportunities available here.
Question four
An investor buys European call on a share for sh 5. The share price is sh 90 and the strike price
is sh 85. Under which circumstances does the investor make profit? When will the option be
exercised? Draw a diagram to show the variation in the investors profit and the share price at
the maturity of the option.
Question five
It is often said that “options and futures are zero-sum games”. What does this mean?
Suggestion for further reading
Orina S Oruru(2013), “ Financial Risk management” Mustard seed business press first
edition ,
(Main textbook).
Hull John (2012) “Options, Futures and other derivatives”, eighth edition.
Johan De Beer (2011) “Introduction to financial derivatives” Van Schaik publishers,
Pretoria SA.