金融工程导论 讲师： 何志刚，倪禾 * Email: nihe@mail.zjgsu.edu.cn*

金融工程导论

讲师： 何志刚，倪禾 *

Email: nihe@mail.zjgsu.edu.cn*

Reference & Online Resource

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