Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.1
Financial Engineering
金融工程学
Textbook,John C,Hull,Options,Futures and Other
Derivative Securities,Prentice Hall,4th Ed.(清华大学出版社,)
New Edition,5th,
第三版中译本：张陶伟，华夏出版社,2000
Hull’s homepage,htpp://www.rotman.utoronto.ca/~hull
to download slides and software
My homepage,http://webpc.shnu.edu.cn/yctang
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.2References
John C,Hull,Fundamentals of Futures and Options Markets,
Prentice Hall,4th Ed.,2002.(清华大学出版社 )
Robert W,Kolb,Futures,Options and Swaps,Blackwell
Publishing,4th Ed.,2002.
Lawrence Galitz,Financial Engineering,Tools and Techniques
to Manage Financial Risks,Pitman Publishing,1995,
(中译本：唐旭，经济科学出版社,1998）
John F,Mrshall,Vipul K,Bansal,Financial Engineering,Simon
& Schuster,1992.
(中译本：宋逢明，朱宝宪，清华大学出版社,1998）
李森，期权理论与案例分析：一个战略性的投资，复旦大学出版社,2002年 8月,
张志强，期权理论与公司理财，华夏出版社,1999.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.3
Introduction
Chapter 1
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.4
The Nature of Derivatives
A derivative（衍生产品 /工具） is
an instrument whose value
depends on the values of other
more basic underlying（标的 /原生）
variables
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.5
Examples of Derivatives
Forward Contracts(远期合约 )
Futures Contracts (期货合约 )
Swaps(互换 )
Options（期权）
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.6
Derivatives Markets
Exchange (交易所 )traded
– Traditionally exchanges have used the open-
outcry system,but increasingly they are
switching to electronic trading
– Contracts are standard and there is virtually no
credit risk
Over-the-counter (OTC，场外市场 )
– A computer- and telephone-linked network of
dealers at financial institutions,corporations,
and fund managers
– Contracts can be non-standard and there is
some small amount of credit risk
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.7
Ways Derivatives are Used
To hedge(规避 ) risks
To speculate(投机 ) (take a view on the
future direction of the market)
To lock in(锁定 ) an arbitrage(套利 ) profit
To change the nature of a liability(负债 )
To change the nature of an investment
without incurring the costs of selling one
portfolio(投资组合 ) and buying another
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.8
Forward Contracts(远期合约 )
A forward contract is an agreement(协议 ) to buy or sell an asset at a certain
time in the future for a certain price
(the delivery price，交割价格 )
It can be contrasted with a spot
contract (现货合约 )which is an
agreement to buy or sell immediately
It is traded in the OTC market
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.9
Foreign Exchange Quotes for
GBP on Aug 16,2001 (See page 3)
Bid(出价 ) Offer(报价 )
Spot 1.4452 1.4456
1-month forward 1.4435 1.4440
3-month forward 1.4402 1.4407
6-month forward 1.4353 1.4359
12-month forward 1.4262 1.4268
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.10
Terminologies
The party that has agreed to buy has
what is termed a long position(多头 )
The party that has agreed to sell has
what is termed a short position(空头 )
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.11
Example (page 3)
On August 16,2001 the treasurer of a
corporation enters into(签署 ) a long forward
contract(多头远期合约 ) to buy ￡1 million in
six months at an exchange rate of 1.4359
This obligates the corporation to pay
$1,435,900 for ￡1 million on February 16,
2002
What are the possible outcomes?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.12
Payoff(损益 ) from a
Long Forward Position
Profit
Price of Underlying
at Maturity,STK
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.13
Payoff from a
Short Forward Position
Profit
Price of Underlying
at Maturity,STK
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.14
Futures Contracts (期货合约 )
Agreement to buy or sell an asset for a
certain price at a certain time
Similar to forward contract
Whereas a forward contract is traded
OTC,a futures contract is traded on an
exchange
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.15
1,Gold,An Arbitrage
Opportunity?
Suppose that:-
The spot price of gold is US$300-
The 1-year forward price of gold
is US$340-
The 1-year US$ interest rate is
5% per annum?
Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.16
2,Gold,Another Arbitrage
Opportunity?
Suppose that:
- The spot price of gold is US$300
- The 1-year forward price of gold is
US$300
- The 1-year US$ interest rate is 5%
per annum
Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.17
The Forward Price of Gold
If the spot price of gold is S and the forward
price for a contract deliverable in T years is
F,then
F = S (1+r )T
where r is the 1-year (domestic currency)
risk-free rate of interest.
In our examples,S = 300,T = 1,and r =0.05
so that
F = 300(1+0.05) = 315
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.18
1,Oil,An Arbitrage
Opportunity?
Suppose that:-
The spot price of oil is US$19-
The quoted 1-year futures price of oil is
US$25-
The 1-year US$ interest rate is 5% per
annum-
The storage costs of oil are 2% per annum
Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.19
2,Oil,Another Arbitrage
Opportunity?
Suppose that:-
The spot price of oil is US$19-
The quoted 1-year futures price of
oil is US$16-
The 1-year US$ interest rate is 5%
per annum-
The storage costs of oil are 2% per
annum
Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.20
Examples of Futures Contracts
Agreement to:
–buy 100 oz,of gold @
US$300/oz,in December
(COMEX)
–sell ￡62,500 @ 1.5000 US$/￡ in
March (CME)
–sell 1,000 bbl,of oil @
US$20/bbl,in April (NYMEX)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.21
Options
A call option(看涨期权 ) is an option to
buy a certain asset
by a certain date for
a certain price (the
strike price，执行价格 /敲定价格 )
A put option(看跌期权 ) is an option to
sell a certain asset
by a certain date for
a certain price (the
strike price)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.22
An American options can be exercised
at any time during its life
A European option can be exercised
only at maturity
American vs European Options
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.23
Examples,Cisco Options
(May 8,2000; Stock Price=62.75)
Strike
Price
July Call Oct Call July Put Oct Put
50 16.87 18.87 2.69 4.62
65 7.00 10.87 8.25 10.62
80 2.00 5.00 17.50 19.50
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.24
Long Call on Microsoft (Figure 1.2,Page 7)
Profit from buying a European(欧式 ) call option on
Microsoft,option price = $5,strike price = $60
30
20
10
0
-5
30 40 50 60
70 80 90
Profit ($)
Terminal
stock price ($)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.25
Short Call on Microsoft (Figure 1.4,page 9)
Profit from writing a European call option on Microsoft,
option price = $5,strike price = $60
-30
-20
-10
0
5
30 40 50 60
70 80 90
Profit ($)
Terminal
stock price ($)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.26
Long Put on IBM (Figure 1.3,page 8)
Profit from buying a European put option on IBM,
option price = $7,strike price = $90
30
20
10
0
-7 90807060 100 110 120
Profit ($)
Terminal
stock price ($)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.27
Short Put on IBM (Figure 1.5,page 9)
Profit from writing a European put option on IBM,
option price = $7,strike price = $90
-30
-20
-10
7
0 90
807060
100 110 120
Profit ($) Terminal
stock price ($)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.28Payoffs(损益 ) from Options
What is the Option Position in Each Case?
K = Strike price,ST = Price of asset at maturity
Payoff Payoff
ST STK
K
Payoff Payoff
ST STK
K
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.29
Options vs,Futures/Forwards
A futures/forward contract gives the
holder the obligation to buy or sell at a
certain price
An option gives the holder the right to
buy or sell at a certain price
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.30
Types of Traders
Hedgers(套期保值者 )
Speculators(投机者 )
Arbitrageurs(套利者 )
Some of the large trading losses in derivatives
occurred because individuals who had a
mandate(授权 ) to hedge risks switched to being
speculators
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.31
Hedging Examples
A US company will pay ￡10 million for imports
from Britain in 3 months and decides to hedge
using a long position in a forward contract (The
3-month forward exchange rate is 1.6056),
What are the alternative strategies?
An investor owns 1,000 Microsoft shares
currently worth $73 per share,A two-month put
with a strike price of $65 costs $2.50,The
investor decides to hedge by buying 10
contracts
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.32
Differences in the two hedge
alternatives
Forward contracts are designed to neutralize
risk by fixing the price that the hedger will
pay or receive for the underlying asset,
There is no assurance that the outcome with
hedging is better than the outcome without
hedging.
The hedge using forward contract requires
no initial payment
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.33
Option contracts provide assurance,They
offer a way for investors to protect
themselves against adverse price movements
in the future while still allowing them to
benefit from favorable price movements.
Option involve the payment of an up-front
fee,
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.34
Speculation Example 1
An investor feels that sterling will
strengthen relative to the U.S,dollar
over the next two months,The current
rate is 1.6470$/ ￡and the 2-month
futures price is 1.6410 $/ ￡.
What are the alternative strategies?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.35
Two strategies:
1,Buy ￡250,000 for $411,750,deposit the
sterling in an interest-earning account
for two months,
2,Take a long position in 4 two-month
futures contracts on sterling (each for
￡62,500).
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.36
Possible outcomes
1,Exchange rate is 1.7000 in two months,The
investor makes $(1.7000-
1.6470)x250,000=$13,250 using the first
strategy and $(1.7000-1.6410)
x250000=$14,750 using the second strategy,
2,Exchange rate is 1.6000 in two month,The
investor has a loss of $(1.6470-
1.6000)x25000=$11,750 using the first
strategy and $(1.6410-1.6000)x25000
=$10,250 using the second strategy.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.37
Speculation Example 2
An investor with $4,000 to invest feels
that the price of Amazon.com will
increase over the next 2 months,The
current stock price is $40 and the price
of a 2-month call option with a strike of
45 is $2
What are the alternative strategies?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.38
Two strategies:
1,Buy 100 shares of Amazon.com.
2,Buy 2,000 2-month call options
(i.e,20 contracts) on Amazon.com
with a $45 strike price.
The cost of each alternative is $4,000.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.39
Possible outcomes
1,Amazon.com rises to $70 two months
later,The Investor makes a profit of
$100x(70-40)=$3,000 using the first
strategy and $2,000 x(70-45)-
$2,000x2=$46,000 using the second.
2,Amazon.com falls to $30 two months
later,The investor losses $100x(40-
30)=$1,000 with the first strategy and
$4,000 with the second strategy.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.40
A Comparison
Both futures and options contracts provide
a way in which a type of leverage can be
obtained (compared with the spot market),
Good outcomes becomes very good,while
bad outcomes become very bad.
In example1,the first alternative requires
an up-front investment of $411,750 while
the second alternative only requires a small
amount say,$25,000 (deposited in a
margin account),In example 2,the profit
(loss) from the second strategy is over 15
(4) times as much as the first.
Leverage,with a relativelu small
initial money,the investor is able to
take a large speculative position.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.41
In the futures setting,the speculator’s
potential loss as well as the potential
gain is very large
In the options setting,no matter how
bad things get,the speculator’s loss is
limited to the cost of the options
(premium)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.42
Arbitrage Example (pages 14)
A stock price is quoted as ￡100 in
London and $172 in New York
The current exchange rate is 1.7500
What is the arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.43
No Arbitrage Assumption
The forces of supply and demand
=>Arbitrage opportunities cannot last
long
=>Assumption,there are no arbitrage
opportunities
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.44
Summary (page 15)
Manual,see pages 471-474 of the book:
John C,Hull,Fundamentals of Futures
and Options Markets,Prentice Hall,4th
Ed.,2002.(清华大学出版社 )
Software,DerivaGem
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.45
Assignments
(page 16-18,4th edition)
1.5,1.9,1.17,1.20,1.21
Tang Yincai,? 2005
1.1
Financial Engineering
金融工程学
Textbook,John C,Hull,Options,Futures and Other
Derivative Securities,Prentice Hall,4th Ed.(清华大学出版社,)
New Edition,5th,
第三版中译本：张陶伟，华夏出版社,2000
Hull’s homepage,htpp://www.rotman.utoronto.ca/~hull
to download slides and software
My homepage,http://webpc.shnu.edu.cn/yctang
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.2References
John C,Hull,Fundamentals of Futures and Options Markets,
Prentice Hall,4th Ed.,2002.(清华大学出版社 )
Robert W,Kolb,Futures,Options and Swaps,Blackwell
Publishing,4th Ed.,2002.
Lawrence Galitz,Financial Engineering,Tools and Techniques
to Manage Financial Risks,Pitman Publishing,1995,
(中译本：唐旭，经济科学出版社,1998）
John F,Mrshall,Vipul K,Bansal,Financial Engineering,Simon
& Schuster,1992.
(中译本：宋逢明，朱宝宪，清华大学出版社,1998）
李森，期权理论与案例分析：一个战略性的投资，复旦大学出版社,2002年 8月,
张志强，期权理论与公司理财，华夏出版社,1999.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.3
Introduction
Chapter 1
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.4
The Nature of Derivatives
A derivative（衍生产品 /工具） is
an instrument whose value
depends on the values of other
more basic underlying（标的 /原生）
variables
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.5
Examples of Derivatives
Forward Contracts(远期合约 )
Futures Contracts (期货合约 )
Swaps(互换 )
Options（期权）
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.6
Derivatives Markets
Exchange (交易所 )traded
– Traditionally exchanges have used the open-
outcry system,but increasingly they are
switching to electronic trading
– Contracts are standard and there is virtually no
credit risk
Over-the-counter (OTC，场外市场 )
– A computer- and telephone-linked network of
dealers at financial institutions,corporations,
and fund managers
– Contracts can be non-standard and there is
some small amount of credit risk
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.7
Ways Derivatives are Used
To hedge(规避 ) risks
To speculate(投机 ) (take a view on the
future direction of the market)
To lock in(锁定 ) an arbitrage(套利 ) profit
To change the nature of a liability(负债 )
To change the nature of an investment
without incurring the costs of selling one
portfolio(投资组合 ) and buying another
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.8
Forward Contracts(远期合约 )
A forward contract is an agreement(协议 ) to buy or sell an asset at a certain
time in the future for a certain price
(the delivery price，交割价格 )
It can be contrasted with a spot
contract (现货合约 )which is an
agreement to buy or sell immediately
It is traded in the OTC market
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.9
Foreign Exchange Quotes for
GBP on Aug 16,2001 (See page 3)
Bid(出价 ) Offer(报价 )
Spot 1.4452 1.4456
1-month forward 1.4435 1.4440
3-month forward 1.4402 1.4407
6-month forward 1.4353 1.4359
12-month forward 1.4262 1.4268
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.10
Terminologies
The party that has agreed to buy has
what is termed a long position(多头 )
The party that has agreed to sell has
what is termed a short position(空头 )
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.11
Example (page 3)
On August 16,2001 the treasurer of a
corporation enters into(签署 ) a long forward
contract(多头远期合约 ) to buy ￡1 million in
six months at an exchange rate of 1.4359
This obligates the corporation to pay
$1,435,900 for ￡1 million on February 16,
2002
What are the possible outcomes?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.12
Payoff(损益 ) from a
Long Forward Position
Profit
Price of Underlying
at Maturity,STK
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.13
Payoff from a
Short Forward Position
Profit
Price of Underlying
at Maturity,STK
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.14
Futures Contracts (期货合约 )
Agreement to buy or sell an asset for a
certain price at a certain time
Similar to forward contract
Whereas a forward contract is traded
OTC,a futures contract is traded on an
exchange
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.15
1,Gold,An Arbitrage
Opportunity?
Suppose that:-
The spot price of gold is US$300-
The 1-year forward price of gold
is US$340-
The 1-year US$ interest rate is
5% per annum?
Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.16
2,Gold,Another Arbitrage
Opportunity?
Suppose that:
- The spot price of gold is US$300
- The 1-year forward price of gold is
US$300
- The 1-year US$ interest rate is 5%
per annum
Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.17
The Forward Price of Gold
If the spot price of gold is S and the forward
price for a contract deliverable in T years is
F,then
F = S (1+r )T
where r is the 1-year (domestic currency)
risk-free rate of interest.
In our examples,S = 300,T = 1,and r =0.05
so that
F = 300(1+0.05) = 315
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.18
1,Oil,An Arbitrage
Opportunity?
Suppose that:-
The spot price of oil is US$19-
The quoted 1-year futures price of oil is
US$25-
The 1-year US$ interest rate is 5% per
annum-
The storage costs of oil are 2% per annum
Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.19
2,Oil,Another Arbitrage
Opportunity?
Suppose that:-
The spot price of oil is US$19-
The quoted 1-year futures price of
oil is US$16-
The 1-year US$ interest rate is 5%
per annum-
The storage costs of oil are 2% per
annum
Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.20
Examples of Futures Contracts
Agreement to:
–buy 100 oz,of gold @
US$300/oz,in December
(COMEX)
–sell ￡62,500 @ 1.5000 US$/￡ in
March (CME)
–sell 1,000 bbl,of oil @
US$20/bbl,in April (NYMEX)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.21
Options
A call option(看涨期权 ) is an option to
buy a certain asset
by a certain date for
a certain price (the
strike price，执行价格 /敲定价格 )
A put option(看跌期权 ) is an option to
sell a certain asset
by a certain date for
a certain price (the
strike price)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.22
An American options can be exercised
at any time during its life
A European option can be exercised
only at maturity
American vs European Options
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.23
Examples,Cisco Options
(May 8,2000; Stock Price=62.75)
Strike
Price
July Call Oct Call July Put Oct Put
50 16.87 18.87 2.69 4.62
65 7.00 10.87 8.25 10.62
80 2.00 5.00 17.50 19.50
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.24
Long Call on Microsoft (Figure 1.2,Page 7)
Profit from buying a European(欧式 ) call option on
Microsoft,option price = $5,strike price = $60
30
20
10
0
-5
30 40 50 60
70 80 90
Profit ($)
Terminal
stock price ($)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.25
Short Call on Microsoft (Figure 1.4,page 9)
Profit from writing a European call option on Microsoft,
option price = $5,strike price = $60
-30
-20
-10
0
5
30 40 50 60
70 80 90
Profit ($)
Terminal
stock price ($)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.26
Long Put on IBM (Figure 1.3,page 8)
Profit from buying a European put option on IBM,
option price = $7,strike price = $90
30
20
10
0
-7 90807060 100 110 120
Profit ($)
Terminal
stock price ($)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.27
Short Put on IBM (Figure 1.5,page 9)
Profit from writing a European put option on IBM,
option price = $7,strike price = $90
-30
-20
-10
7
0 90
807060
100 110 120
Profit ($) Terminal
stock price ($)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.28Payoffs(损益 ) from Options
What is the Option Position in Each Case?
K = Strike price,ST = Price of asset at maturity
Payoff Payoff
ST STK
K
Payoff Payoff
ST STK
K
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.29
Options vs,Futures/Forwards
A futures/forward contract gives the
holder the obligation to buy or sell at a
certain price
An option gives the holder the right to
buy or sell at a certain price
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.30
Types of Traders
Hedgers(套期保值者 )
Speculators(投机者 )
Arbitrageurs(套利者 )
Some of the large trading losses in derivatives
occurred because individuals who had a
mandate(授权 ) to hedge risks switched to being
speculators
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.31
Hedging Examples
A US company will pay ￡10 million for imports
from Britain in 3 months and decides to hedge
using a long position in a forward contract (The
3-month forward exchange rate is 1.6056),
What are the alternative strategies?
An investor owns 1,000 Microsoft shares
currently worth $73 per share,A two-month put
with a strike price of $65 costs $2.50,The
investor decides to hedge by buying 10
contracts
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.32
Differences in the two hedge
alternatives
Forward contracts are designed to neutralize
risk by fixing the price that the hedger will
pay or receive for the underlying asset,
There is no assurance that the outcome with
hedging is better than the outcome without
hedging.
The hedge using forward contract requires
no initial payment
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.33
Option contracts provide assurance,They
offer a way for investors to protect
themselves against adverse price movements
in the future while still allowing them to
benefit from favorable price movements.
Option involve the payment of an up-front
fee,
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.34
Speculation Example 1
An investor feels that sterling will
strengthen relative to the U.S,dollar
over the next two months,The current
rate is 1.6470$/ ￡and the 2-month
futures price is 1.6410 $/ ￡.
What are the alternative strategies?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.35
Two strategies:
1,Buy ￡250,000 for $411,750,deposit the
sterling in an interest-earning account
for two months,
2,Take a long position in 4 two-month
futures contracts on sterling (each for
￡62,500).
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.36
Possible outcomes
1,Exchange rate is 1.7000 in two months,The
investor makes $(1.7000-
1.6470)x250,000=$13,250 using the first
strategy and $(1.7000-1.6410)
x250000=$14,750 using the second strategy,
2,Exchange rate is 1.6000 in two month,The
investor has a loss of $(1.6470-
1.6000)x25000=$11,750 using the first
strategy and $(1.6410-1.6000)x25000
=$10,250 using the second strategy.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.37
Speculation Example 2
An investor with $4,000 to invest feels
that the price of Amazon.com will
increase over the next 2 months,The
current stock price is $40 and the price
of a 2-month call option with a strike of
45 is $2
What are the alternative strategies?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.38
Two strategies:
1,Buy 100 shares of Amazon.com.
2,Buy 2,000 2-month call options
(i.e,20 contracts) on Amazon.com
with a $45 strike price.
The cost of each alternative is $4,000.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.39
Possible outcomes
1,Amazon.com rises to $70 two months
later,The Investor makes a profit of
$100x(70-40)=$3,000 using the first
strategy and $2,000 x(70-45)-
$2,000x2=$46,000 using the second.
2,Amazon.com falls to $30 two months
later,The investor losses $100x(40-
30)=$1,000 with the first strategy and
$4,000 with the second strategy.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.40
A Comparison
Both futures and options contracts provide
a way in which a type of leverage can be
obtained (compared with the spot market),
Good outcomes becomes very good,while
bad outcomes become very bad.
In example1,the first alternative requires
an up-front investment of $411,750 while
the second alternative only requires a small
amount say,$25,000 (deposited in a
margin account),In example 2,the profit
(loss) from the second strategy is over 15
(4) times as much as the first.
Leverage,with a relativelu small
initial money,the investor is able to
take a large speculative position.
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.41
In the futures setting,the speculator’s
potential loss as well as the potential
gain is very large
In the options setting,no matter how
bad things get,the speculator’s loss is
limited to the cost of the options
(premium)
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.42
Arbitrage Example (pages 14)
A stock price is quoted as ￡100 in
London and $172 in New York
The current exchange rate is 1.7500
What is the arbitrage opportunity?
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.43
No Arbitrage Assumption
The forces of supply and demand
=>Arbitrage opportunities cannot last
long
=>Assumption,there are no arbitrage
opportunities
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.44
Summary (page 15)
Manual,see pages 471-474 of the book:
John C,Hull,Fundamentals of Futures
and Options Markets,Prentice Hall,4th
Ed.,2002.(清华大学出版社 )
Software,DerivaGem
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
1.45
Assignments
(page 16-18,4th edition)
1.5,1.9,1.17,1.20,1.21
