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What is a Derivative?. A derivative is an instrument whose value depends on, or is derived from, the value of another asset. Examples: futures, forwards, swaps, options , exotics…. Why Derivatives Are Important. Derivatives play a key role in transferring risks in the economy

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what is a derivative
What is a Derivative?
  • A derivative is an instrument whose value depends on, or is derived from, the value of another asset.
  • Examples: futures, forwards, swaps, options, exotics…
why derivatives are important
Why Derivatives Are Important
  • Derivatives play a key role in transferring risks in the economy
  • The underlying assets include stocks, currencies, interest rates, commodities, debt instruments, electricity, insurance payouts, the weather, etc
  • Many financial transactions have embedded derivatives
  • The real options approach to assessing capital investment decisions has become widely accepted
how derivatives are traded
How Derivatives Are Traded

On exchanges such as the Chicago Board Options Exchange

In the over-the-counter (OTC) market where traders working for banks, fund managers and corporate treasurers contact each other directly

size of otc and exchange traded markets figure 1 1 page 3
Size of OTC and Exchange-Traded Markets(Figure 1.1, Page 3)

Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market

how derivatives are used
How Derivatives are Used

To hedge risks

To speculate (take a view on the future direction of the market)

To lock in an arbitrage profit

forward price
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 (as shown by the table)

terminology
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

example page 5
Example (page 5)

On May 24, 2010 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 1.4422

This obligates the corporation to pay $1,442,200 for £1 million on November 24, 2010

What are the possible outcomes?

profit from a long forward position k delivery price forward price at time contract is entered into

Profit

Price of Underlying at Maturity, ST

Profit from a Long Forward Position (K= delivery price=forward price at time contract is entered into)

K

slide11

Profit

Price of Underlying

at Maturity, ST

Profit from a Short Forward Position (K= delivery price=forward price at time contract is entered into)

K

futures contracts
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

exchanges trading futures
Exchanges Trading Futures

CME Group (formerly Chicago Mercantile Exchange and Chicago Board of Trade)

NYSE Euronext

BM&F (Sao Paulo, Brazil)

TIFFE (Tokyo)

and many more

examples of futures contracts
Examples of Futures Contracts

Agreement to:

  • Buy 100 oz. of gold @ US$1400/oz. in December
  • Sell £62,500 @ 1.4500 US$/£ in March
  • Sell 1,000 bbl. of oil @ US$90/bbl. in April
1 gold an arbitrage opportunity
1. Gold: An Arbitrage Opportunity?

Suppose that:

The spot price of gold is US$1,400

The 1-year forward price of gold is US$1,500

The 1-year US$ interest rate is 5% per annum

Is there an arbitrage opportunity?

2 gold another arbitrage opportunity
2. Gold: Another Arbitrage Opportunity?

Suppose that:

  • The spot price of gold is US$1,400
  • The 1-year forward price of gold is US$1,400
  • The 1-year US$ interest rate is 5% per annum

Is there an arbitrage opportunity?

the forward price of gold ignores the gold lease rate
The Forward Price of Gold (ignores the gold lease rate)

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 = 1400, T = 1, and r=0.05 so that

F = 1400(1+0.05) = 1470

options
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 option is an option to sell a certain asset by a certain date for a certain price (the strike price)

american vs european options
American vs European Options

An American option can be exercised at any time during its life

A European option can be exercised only at maturity

review of option types
Review of Option Types

A call is an option to buy

A put is an option to sell

A European option can be exercised only at the end of its life

An American option can be exercised at any time

option positions
Option Positions

Long call

Long put

Short call

Short put

long call

Profit ($)

30

20

10

Terminal

stock price ($)

70

80

90

100

0

110

120

130

-5

Long Call

Profit from buying one European call option: option price = $5, strike price = $100, option life = 2 months

short call

Profit ($)

110

120

130

5

0

70

80

90

100

Terminal

stock price ($)

-10

-20

-30

Short Call

Profit from writing one European call option: option price = $5, strike price = $100

long put

Profit ($)

30

20

10

Terminal

stock price ($)

0

40

50

60

70

80

90

100

-7

Long Put

Profit from buying a European put option: option price = $7, strike price = $70

short put

Profit ($)

Terminal

stock price ($)

7

40

50

60

0

70

80

90

100

-10

-20

-30

Short Put

Profit from writing a European put option: option price = $7, strike price = $70

payoffs from options what is the option position in each case
Payoffs from OptionsWhat is the Option Position in Each Case?

Payoff

Payoff

K

K

ST

ST

Payoff

Payoff

K

K

ST

ST

K = Strike price, ST= Price of asset at maturity

assets underlying exchange traded options
Assets UnderlyingExchange-Traded Options

Stocks

Foreign Currency

Stock Indices

Futures

options vs futures forwards
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

types of traders
Types of Traders

Hedgers

Speculators

Arbitrageurs

swaps
Swaps

A swap is an agreement to exchange cash flows at specified future times according to certain specified rules

an example of a plain vanilla interest rate swap
An Example of a “Plain Vanilla” Interest Rate Swap

An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million

Next slide illustrates cash flows that could occur (Day count conventions are not considered)

typical uses of an interest rate swap
Typical Uses of an Interest Rate Swap
  • Converting a liability from
    • fixed rate to floating rate
    • floating rate to fixed rate
  • Converting an investment from
    • fixed rate to floating rate
    • floating rate to fixed rate