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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…
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Why Derivatives Are ImportantDerivatives 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
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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
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Size of OTC and Exchange-Traded Markets(Figure 1.1, Page 3)
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Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market
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How Derivatives are UsedTo hedge risks
To speculate (take a view on the future direction of the market)
To lock in an arbitrage profit
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Foreign Exchange Quotes for GBP, May 24, 2010
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Bid Offer
Spot 1.4407 1.4411
1-month forward 1.4408 1.4413
3-month forward 1.4410 1.4415
6-month forward 1.4416 1.4422
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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)
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TerminologyThe 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
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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?
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Profit from a Long Forward Position (K= delivery price=forward price at time contract is entered into)
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Profit
Price of Underlying at Maturity, STK
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Profit from a Short Forward Position (K= delivery price=forward price at time contract is entered into)
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Profit
Price of Underlying at Maturity, ST
K
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Futures ContractsAgreement 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
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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
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Examples of Futures ContractsAgreement 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
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1. Gold: An Arbitrage Opportunity?
Suppose that:The spot price of gold is US$1,400The 1-year forward price of gold is US$1,500The 1-year US$ interest rate is 5% per
annum
Is there an arbitrage opportunity?
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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?
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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
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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)
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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
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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
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Option Positions
Long call
Long put
Short call
Short put
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Long Call Profit from buying one European call option: option
price = $5, strike price = $100, option life = 2 months
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30
20
10
0-5
70 80 90 100
110 120 130
Profit ($)
Terminalstock price ($)
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Short Call Profit from writing one European call option: option
price = $5, strike price = $100
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-30
-20
-10
05
70 80 90 100
110 120 130
Profit ($)
Terminalstock price ($)
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Long Put Profit from buying a European put option: option
price = $7, strike price = $70
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30
20
10
0
-770605040 80 90 100
Profit ($)
Terminalstock price ($)
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Short Put Profit from writing a European put option: option price
= $7, strike price = $70
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-30
-20
-10
7
070
605040
80 90 100
Profit ($)Terminal
stock price ($)
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Payoffs from OptionsWhat is the Option Position in Each Case?
K = Strike price, ST = Price of asset at maturity
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Payoff Payoff
ST STKK
PayoffPayoff
ST STKK
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Assets UnderlyingExchange-Traded Options
Stocks
Foreign Currency
Stock Indices
Futures
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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
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Types of Traders
Hedgers
Speculators
Arbitrageurs
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Swaps
A swap is an agreement to exchange cash flows at specified future times according to certain specified rules
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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)
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One Possible Outcome for Cash Flows to Microsoft (Table 7.1, page 150)
Date LIBOR Floating Cash Flow
Fixed Cash Flow
Net Cash Flow
Mar 5, 2012
4.20%
Sep 5, 2012
4.80% +2.10 −2.50 −0.40
Mar 5, 2013
5.30% +2.40 −2.50 −0.10
Sep 5, 2013
5.50% +2.65 −2.50 + 0.15
Mar 5, 2014
5.60% +2.75 −2.50 +0.25
Sep 5, 2014
5.90% +2.80 −2.50 +0.30
Mar 5, 2015
+2.95 −2.50 +0.45
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Typical Uses of an Interest Rate Swap
Converting a liability fromfixed rate to floating rate floating rate to fixed rate
Converting an investment from fixed rate to floating ratefloating rate to fixed rate
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