Transcript An Introduction to Derivative Markets and Securities

Chapter 11
An Introduction to Derivative
Markets and Securities
Innovative Financial Instruments
Dr. A. DeMaskey
Learning Objectives
Questions to be answered:





What are derivative securities?
What are the basic types of derivative securities and the
terminology associated with them?
What are the similarities and differences in the payoff
structures created by each of the derivative instruments?
How are forward contracts, put options and call options
related?
What are the uses of derivative contracts?
Derivative Instruments



The value depends directly on, or is derived from,
the value of another security or commodity, called
the underlying asset.
Forward and Futures contracts are agreements
between two parties - the buyer agrees to purchase
an asset from the seller at a specific date at a price
agreed to now.
Options offer the buyer the right without
obligation to buy or sell at a fixed price up to or on
a specific date.
Why Do Derivatives Exist?
Assets are traded in the cash or spot market.
 It is sometimes advantageous to enter into a
transaction now with the exchange of the
asset and payment taking place at a future
time.
 Risk shifting
 Price formation
 Investment cost reduction

Characteristics of Derivative
Instruments



Forward contracts are the right and full obligation to
conduct a transaction involving another security or
commodity - the underlying asset - at a predetermined date
(maturity date) and at a predetermined price (contract
price). This is a trade agreement.
Futures contracts are similar, but subject to margin
requirements and daily settlement.
Options give the holder the right to either buy or sell a
specified amount of the underlying asset at a specified
price within a specified period of time.
Forward Contracts
 Buyer
is long, seller is short
 Contracts have negotiable terms and
are traded in the OTC market
 Subject to credit risk or default risk
 No payments until expiration
 Agreement may be illiquid
Payoff Structure to Long and
Short Forward Positions
Long Forward
Profit
Long
Gain
Short
Gain
0
S1
Long
Loss
Loss
F0,T
S2
St
Short
Loss
Short Forward
Futures Contracts
 Standardized
terms
 Central market (futures exchange)
 More liquidity
 Less liquidity risk due to initial margin
 Daily settlement called “marking-tomarket”
Option Contracts




Holder vs. Grantor
Call Option vs. Put
Option
Exercise or Strike
Price
Premium




American Option vs.
European Option
At-The-Money Option
In-The-Money Option
Out-Of-The Money
Option
Option Pricing and Valuation

An option’s value consists of two parts:
–
–
Intrinsic Value
Time Value
Intrinsic Value is the amount by which an
option is in-the-money
 Time Value is the amount by which an
option’s value exceeds its intrinsic value

To Illustrate:

Suppose the current stock price is 50. The premium on a
call option with an exercise price of 48 is $5.25.
–
–
What is the intrinsic value (IV)?
What is the time value (TV)?
Call Option Value
Total value
of option
Time value
Intrinsic value
Out-of-the-money E
In-the-money
Spot Rate
Basic Pricing Relationships





Call options are always worth at least the intrinsic
value.
The lower the exercise price, the greater the call
option’s premium.
The longer the time to expiration, the greater the
value of any option.
The greater the volatility of the underlying asset,
the greater the value of any option.
American options are at least as valuable as
European options.
Option Pricing Relationships
Factor
Call Option
Stock price
+
Exercise price
Time to expiration
+
Interest rate
+
Volatility of underlying asset +
Where: + = positive or direct relationship
- = negative or inverse relationship
Put Option
+
+
+
Profits to Buyer of Call Option
3,000
Profit from Strategy
2,500
Exercise Price = $70
2,000
Option Price
= $6.125
1,500
1,000
500
0
(500)
(1,000)
40
Stock Price at
Expiration
50
60
70
80
90
100
Profits to Seller of Call Option
1,000
Profit from Strategy
Exercise Price = $70
500
Option Price
Limited Gain
0
= $6.125
X=70
(500)
Potentially
Unlimited
Loss
Breakeven price
(1,000)
(1,500)
(2,000)
(2,500)
(3,000)
40
Stock Price at
Expiration
50
60
70
80
90
100
Profits to Buyer of Put Option
3,000
Profit from Strategy
2,500
2,000
Exercise Price = $70
1,500
Option Price
= $2.25
1,000
500
0
Stock Price at
Expiration
(500)
(1,000)
40
50
60
70
80
90
100
Profits to Seller of Put Option
1,000
Profit from Strategy
500
Breakeven price
Limited Gain
0
(500)
(1,000)
X=70
Potentially
Limited
Loss
Exercise Price = $70
Option Price
= $2.25
(1,500)
(2,000)
(2,500)
(3,000)
40
Stock Price at
Expiration
50
60
70
80
90
100
Investing with Derivative
Securities
 Forward
–
–
does not require front-end payment
requires future settlement payment
 Option
–
–
contract
contract
requires up front payment
allows but does not require future
settlement payment
Put-Call-Spot Parity
A. Net Portfolio Investment at Initiation (Time 0)
Portfolio
Long 1 WZY Stock
S0
Long 1 Put Option
P0,T
Short 1 Call Option
-C 0,T
Net Investment
S0 + P0,T - C 0,T
B. Portfolio Value at Option Expiration (Time T)
Portfolio
If ST  X
If ST > X
Long 1 WZY Stock
ST
ST
Long 1 Put Option
(X - ST)
0
Short 1 Call Option
0
-(ST - X)
Net Position
X
X
Put-Call-Spot Parity
The net position is a guaranteed contract;
that is, it is riskfree.
 Since the riskfree rate equals the T-bill rate,
the no-arbitrage condition can be shown as:

(long stock)+(long put)+(short call)=(long T-bill)
S0  P0,T  C0,T
X

(1  RFR)T
Application of Put-Call Parity
If securities are properly valued, the net
position has a value of zero.
 Put-call-spot parity can be used to check if
calls and puts are properly priced relative to
each other.
 Any mispricing of calls and puts offer
arbitrage opportunities.

Creating Synthetic Securities
Using Put-Call-Spot Parity

A riskfree portfolio could be created by
combining three risky securities:
–
–
–

a stock
a put option,
and a call option
With the Treasury-bill as the fourth security,
any one of the four may be replaced with
combinations of the other three
Replicating a Put Option
A. Net Portfolio Investment at Initiation (Time 0)
Portfolio
Long 1 T-Bill
X(1 + RFR)-T
Short 1 XYZ Stock
-S0
Long 1 Call Option
C 0,T
Net Investment
X(1 + RFR)-T - S0 + C 0,T
B. Portfolio Value at Option Expiration (Time T)
Portfolio
If ST  X
If ST > X
Long 1 T-Bill
X
X
Short 1 XYZ Stock
- ST
-ST
Long 1 Call Option
0
(ST - X)
Net Position
X - ST
0
Adjusting Put-Call Spot Parity
For Dividends

If a stock pays a dividend, DT, immediately
prior to expiration of the options, put-call
parity is modified as follows:
S0  P0,T  C0,T
or
X  DT

(1  RFR)T
DT
X
S0 
 P0,T  C0,T 
T
(1  RFR)
(1  RFR)T
Put-Call-Forward Parity
Instead of buying stock, take a long position
in a forward contract to buy stock.
 Supplement this transaction by purchasing a
put option and selling a call option, each
with the same exercise price and expiration
date.
 This reduces the net initial investment
compared to purchasing the stock in the
spot market.

Put-Call-Forward Parity
A. Net Portfolio Investment at Initiation (Time 0)
Portfolio
Long 1 Forward Contract
0
Long 1 Put Option
P0,T
Short 1 Call Option
-C 0,T
Net Investment
P0,T - C 0,T
B. Portfolio Value at Option Expiration (Time T)
Portfolio
If ST  X
If ST > X
Long 1 Forward Contract ST - F0,T
ST - F0,T
Long 1 Put Option
(X - ST)
0
Short 1 Call Option
0
-(ST - X)
Net Position
X - F0,T
X - F0,T
Put-Call-Forward Parity
P0,T  C0,T
X  F0,T

(1  RFR)T
If this condition does not hold, then there
are opportunities for arbitrage.
 If the stock pays a dividend at times T, the
condition becomes:

F0,T
DT
S0 

T
(1  RFR)
(1  RFR)T
Restructuring Asset Portfolios
with Forward Contracts


Tactical asset allocation to time general market
movements instead of company-specific trends.
Direct Method:
–

Indirect Method:
–

Sell stock in open market and buy T-bills
Short forward contracts against a long position in
underlying asset
Benefits:
–
–
–
Quicker and cheaper
Neutralizes risk of falling stock price
Converts beta of stock to zero
Dynamics of Hedge
Economic
Event
ff
Actual
Stock
Exposure
Desired
Forward
Exposure
Stock
prices fall
Loss
Gain
Stock
prices rises
Gain
Loss
Protecting Portfolio Value
with Put Options

Protective Puts
–
–
–

Hedge potential drop in value of underlying
asset
Keep from committing to sell if price rises
Asymmetric hedge
Portfolio Insurance
–
–
Hold the shares and purchase a put option, or
Sell the shares and buy a T-bill and a call option
Dynamics of Hedge
Actual
Economic Stock
Event
Exposure
ff
Desired
Hedge
Exposure
Stock
prices fall
Loss
Gain
Stock
prices rises
Gain
No Loss
The Internet
Investments Online
www.cboe.com
www.cbot.com
www.cme.com
www.cme.com/educational/hand1.htm
www.liffe.com
www.options-iri.com