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金融工程 郑振龙 高等教育出版社 Options, Futures and other derivatives
John C. Hull Prentice Hall
Bloomberg: http://www.bloomberg.com Wall Street Jounral: http://online.wsj.com Financial Times: http://www.ft.com Reuters: http://www.reuters.com
Introduction What is finance
What is financial engineering
Why financial engineering
Financial Engineering Emergence
1. Oil price: OPEC 2. Fixed – Floating foreign exchange rat
e: Bretton Wood system 3. Interests rate – inflation rate
Financial Engineering Development
Advanced information technology Pricing, Fast process, Globel market
Efficiency of financial markets Gain profits and hedge risks
Financial Engineering and Risk Management
Risk managemant is the key of FE Transfer risk i.e. Forward Split risk i.e. Portfolio
The Nature of Derivatives A derivative is an instrument
whose value depends on the values of other more basic underlying variables
Examples of Derivatives
Forward Contracts Futures Contracts Options Swaps
Derivatives Markets Exchange Traded
standard products trading floor or computer trading virtually no credit risk
Over-the-Counter non-standard products telephone market some credit risk
Ways Derivatives are Used
To hedge risks To reflect a view on the future directi
on of the market To lock in profit To change the nature of a liability To change the nature of an investmen
t without incurring the costs of selling one portfolio and buying another
Forward Contracts A forward contract is an agreement t
o buy or sell an asset at a certain time in the future for a certain price (the delivery price)
A spot contract is an agreement to buy or sell immediately
How a Forward Contract Works
The contract is an over-the-counter (OTC) agreement between 2 companies
The delivery price is usually chosen so that the initial value of the contract is zero
No money changes hands when contract is first negotiated and it is settled at maturity
The Forward Price The forward price for a contract is
the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero)
The forward price may be different for contracts of different maturities
Terminology The party that has agreed to buy
has what is termed a long position The party that has agreed to sell
has what is termed a short position
Examples On January 20, 1998 a trader
enters into an agreement to buy £1 million in three months at an exchange rate of 1.6196
This obligates the trader to pay $1,619,600 for £1 million on April 20, 1998
What are the possible outcomes?
Profit from a Forward Position
K
Price of Underlying at Maturity, ST
Profit
ST
Long Position
Short Position
Gain
Loss
Price
Futures Contracts 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
Arbitrage Opportunity (I)
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?
Arbitrage Opportunity (II)
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?
The Forward Price of Gold
If the spot price of gold is S , 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
Arbitrage Opportunity (III)
Suppose that: The spot price of oil is US$20 The quoted 1-year futures price of oil is
US$25 The 1-year US$ interest rate is 5% per an
num The storage costs of oil are 2% per annu
m Is there an arbitrage opportunity?
Arbitrage Opportunity (IV) Suppose that:
The spot price of oil is US$20 The quoted 1-year futures price of oil is
US$21 The 1-year US$ interest rate is 5% per an
num The storage costs of oil are 2% per annu
m Is there an arbitrage opportunity?
Exchanges Trading Futures
Chicago Board of Trade Chicago Mercantile Exchange BM&F (Sao Paulo, Brazil) LIFFE (London) TIFFE (Tokyo)
Options A call option is an option to buy a
certain asset by a certain date for a certain price (the strike price)
A put is an option to sell a certain asset by a certain date for a certain price (the strike price)
Long Call on IBM Profit from buying an IBM
European call option: option price = $5, strike price = $100, option life = 2 months30
20
10
0-5
70 80 90 100
110 120 130
Profit ($)
Terminalstock price ($)
Short Call on IBM Profit from writing an IBM
European call option: option price = $5, strike price = $100, option life = 2 months
-30
-20
-10
05
70 80 90 100
110 120 130
Profit ($)
Terminalstock price ($)
Long Put on Exxon Profit from buying an Exxon Europe
an put option: option price = $7, strike price = $70, option life = 3 mths30
20
10
0
-770605040 80 90 100
Profit ($)
Terminalstock price ($)
Short Put on Exxon Profit from writing an Exxon Europe
an put option: option price = $7, strike price = $70, option life = 3 mths
-30
-20
-10
7
070
605040
80 90 100
Profit ($)Terminal
stock price ($)
Payoffs from Options
What is the Option Position in Each Case? X = Strike price, ST = Price of asset at maturity
Payoff Payoff
ST STXX
Payoff Payoff
ST STXX
Swaps Definition: A derivative in which two co
unterparties agree to exchange one stream of cash flows against another stream.
Objective: Hedge certain risks such as interest rate risk
Fixed-to-floating interest rate swap
Fixed Rate Floating Rate
Company A
9 % LIBOR + 0.4%
Company B
12 % LIBOR + 1.2%
Fixed-to-floating interest rate swap
Benefit from comparative advantage
9% + LIBOR + 1.2% = 10.2 % + LIBOR12% + LIBOR + 0.4 % = 12.4% + LIBOR
LIBOR: London inter bank offer rate
Types of Traders Hedgers Speculators Arbitrageurs Some of the large trading losses in
derivatives occurred because individuals who had a mandate to hedge risks switched to being speculators
Hedging Examples A US company will pay £1 million for impor
ts from Britain in 3 months and decides to hedge using a long position in a forward contract
An investor owns 500 IBM shares currently worth $102 per share. A two- month put with a strike price of $100 costs $4. The investor decides to hedge by buying put options
Speculation Example
An investor with $7,800 to invest feels that Exxon’s stock price will increase over the next 3 months. The current stock price is $78 and the price of a 3-month call option with a strike of $80 is $3
Arbitrage Example 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?
Exchanges Trading Options
Chicago Board Options Exchange American Stock Exchange Philadelphia Stock Exchange Pacific Stock Exchange European Options Exchange Australian Options Market
