Derivatives
1
Introduction
• Definition: A derivative security is a financial security
whose payoff is linked to another, previously issued
security (stocks bonds or mortgage backed securities.
• Derivative securities generally involve an agreement
between two parties to exchange a standard quantity of
an asset or cash flow at a pre determined price and at a
specified date in future.
• The markets in which derivative securities are traded are
called derivative security market.
• Derivative market is basically a risk management market.
• Spot contract: It is an agreement of immediate
sale/purchase.
• Forward Contract: vice versa
2
Options
• Currency Options: (it is an insurance against ER risk)
• An option is a contract that allows the holder a right not
an obligation to buy sell a specified currency on a
specified date at a pre determined ER.
Holder/ Buyer
Issuer/Writer
Long Call
Short Call
Long Put
Short Put
Types of Option Contracts:
American
vs
European
Can be exercised on or
Can only be exercised
before a maturity date.
At a fix maturity date.
𝑷𝑨
≥
𝑷𝑼
3
Diagram
Profit
Long Put
Long call
𝑋
0
Loss
90
100
110
𝑆𝑇
4
For Receivables
For Payable
purchase of put option
Purchase of call option
Value of an Option (Intrinsic Value)
Call Option
𝑪𝒖 = 𝑴𝒂𝒙(𝑺𝑻 − 𝑿, 𝟎)
Put Option
𝑷𝒖 = 𝑴𝒂𝒙(𝑿 − 𝑺𝑻 , 𝟎)
Where 𝑿 is the agreed future price of the currency.
𝑺𝑻 is the future ER at the time of exercise.
Profit
Long call
𝑋
0
Loss
90
100
110
𝑆𝑇
5
Diagram
Profit
𝑋
0
Loss
90
100
110
𝑆𝑇
Short Call
Profit
Long Put
𝑋
0
Loss
90
100
6
110
𝑆𝑇
Diagram
Profit
Short Put
0
Loss
𝑿
100
𝑆𝑇
Option Premium:
Option premium = f(Spot price of an asset, Exercise price, Exercise
Date, Price volatility of an Asset, 𝑹𝒇 )
Option premium is consist of two things
i)Intrinsic value
ii) Time value
When the option is in the Money.
Buying of an out of
(it belongs to/it is a part of real nature)
(for call option Stock Price>exercise
price)
Money option on the basis
of probability that it may
come in the money in near
future.
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Option Contract Cont.
• Value of call option always remains greater than forward
purchase contract.
• Call option is nice part of forward purchase contract.
• Put option is the nice part of forward sale contract.
Numerical example:
• Call on us dollar
X=95/$
If spot prices are
𝑺𝑻 = 93 94
95 96 97 98
𝑪𝒖 = 0
0
0
1
2
3
Payoffs of buyer of call option (on the basis
of intrinsic value only)
8
93
94
95
96
97
Option Contract Cont.
• Put on us dollar
If spot prices are
X=95/$
𝑺𝑻 = 93
𝑷𝒖 = 2
94
1
95
0
96
0
97
0
98
0
Main points:
Holder of call: Buying a call is a nice part (beneficial/profitable)
of forward purchase contract i.e. if 𝑺𝑻 > X
Seller of Call: selling a call is a bad part(loss) of the forward sale
contract.
Similarly, Buying a put is a nice part (beneficial/profitable) of
forward sale contract.
Selling a put is a bad part(loss) of the forward purchase
contract.
In short from the holder point of view options are better than
forward contract.
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An Interesting Example
• If someone wants to avoid commission and also wants to
sell receipts of exports at a guaranteed rate then he can
buy put option and sell call option.
• i.e. long put and short call (holder of put option and issue
of call option)
• Suppose X=95
𝑺𝑻 = 93 94
95 96 97 98
P = 2
1
0
0
0
0
-C = 0
0
0
-1 -2 -3
P-C = 2
1
0
-1 -2 -3
𝑿 − 𝑺𝑻 = 2
1
0
-1 -2 -3
P-C = FS
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Examples Cont.
• For Purchase of $s
• long call and short put (holder of put option and issue of call
option)
• Suppose X=95
𝑺𝑻 = 93 94
95 96 97 98
- P = -2
-1
0
0
0
0
C = 0
0
0
1
2
3
C-P = 2
1
0
-1 -2 -3
𝑿 − 𝑺𝑻 = 2
1
0
-1 -2 -3
C-P = FP
Use of Option Contract: Bidding …… we won ….. We have to
pay ….. So option contract is best.
Use of Forward Contract: imports/exports ….. Use forward
Use of Forward Contract: imports/exports ….. Use forward
We use currency option for the purpose of hedging. Hedging is
the avoidence of foreign exchange risk.
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Forward Contract
• Definition: “A forward transection involves an agreement
today to buy or sell a specified amount of a foreign currency
at a specified future date at a predetermined rate”.
• Or “ it is a contract in which two counter parties agree to
exchange a particular asset at a predetermined price at a
specific date.
• Why to go for forward contract?
• Oil mill (Dalda)…. Major input…. Plam oil …. Which is imported
from Malaysia…. If we are expecting that the price of palm oil
(in our domestic currency) will increase due to depreciation of
the domestic currency then our desire must be to avoid ER
risk.
• ER risk can be avoided by purchasing a forward contract.
• Forward contract will only be established if both the parties,
expectations are different.
12
Forward Contract cont.
• Payoff of a forward contract are symmetric or linear in nature.
• If S>X buyer will gain (who bought forward contract)
• If S<X seller will gain (who sold forward contract)
Gain
Seller
0
Buyer
94
X
95
96
Loss
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Forward Contract cont.
• Derivative are used to manage risk (risk of loss)
not the loss.
• Problems attached with forwards.
i) size and settlement date
ii) Illiquid (before maturity we can’t withdraw)
iii) Default risk (gain of one party and loss of
another party. Therefore the party who is
facing loss can default.
14
Future Contract
• Futures are traded in organized exchanges. Therefore,
exchange trade can’t be done without broker.
• Futures are standardized (first problem of size is resolved).
• Futures are traded on exchanges so liquidity problem is
resolved(second problem is resolved).
• What is the need of future when forward are there? Due to the
involvement of broker future contract overcome the problem
of default risk (even the third problem is resolved).
Mr. A
Mr. B
Buyer
Broker
Seller
200*500=100,000
Suppose 30% of contract value is paid/deposited by both parties
and such a deposit is necessary for account opening with broker.
It is called initial margin.
Initial margin varies from market to market.
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Future Contract Cont.
Days
Market Price
Settlement
Balance
Monday
200
-
30,000
Tuesday
208
208-200/200*100,000
34,000
Wednesday
199
199-208/200*100,000
29,500
Thursday
195
195-199/200*100,000
27,500
Friday
190
190-195/200*100,000
25,000
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Future Contract Cont.
• Suppose the maintenance margin is 26% i.e. 26,000.
• Then at a price of 190 buyer of the commodity/ asset will
receive a margin call from the broker to deposit a variation
margin of Rs 5,000 so that once again initial margin can be
achieved. (mc must be met within 12 hours)
Key Terms:
• IM: any amount to establish a future contract is called IM.
• MM: the minimum amount that must be kept in the margin
account is called MM.
• Margin call: call of a broker (in case if margin becomes less than
MM) to deposit a difference the actual margin and MM.
• Variation margin: the amount deposited in response to margin
call is called variation margin.
• Margin to market: the adjustment of margin a/c on daily basis is
called margin to market.
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Future Contract Cont.
• Therefore, initial margin or simply margin is a weapon of the
broker.
• The broker will take the collateral (i.e. full balance as a
penalty)
Key Differences:
Forwards
Non standardized
Self regulated
Cash flow at the time of maturity
Default risk
No liquidity
Futures
Standardized
Exchange regulated
daily basis cash flow
No default risk
Liquidity
18
Swaps
• A swap is an agreement between the two parties to exchange some
cash flow in near future based on some underlying instrument or
price at specific rate. The derivative instrument swaps are used to
manage interest rate, foreign exchange and credit risks.
Interest Rate Swap: (with swap managers of both financial
institutions hedge interest rate risk)
Swap Buyer(agrees to make fix rate
Swap Seller
payments also called principle)
RSA>RSL
RSA<RSL
if interest rate declines then
drop of income from assets is more than the decline in liabilities so
profit declines. After swap RSA by 1 million and RSL by 1 million.
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Currency Swap
• Currency swaps are useful for the purpose of hedging in case if
the firms assets and liabilities are in different currencies.
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