introduction lecture 1
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introductionTRANSCRIPT
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Lecture 1: Introduction
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Gwion Williams
ASB4417/4817 Financial Engineering
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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 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
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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
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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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The Lehman Bankruptcy
Lehmans filed for bankruptcy on September 15, 2008.
This was the biggest bankruptcy in US history
Lehman was an active participant in the OTC derivatives
markets and got into financial difficulties because it took
high risks and found it was unable to roll over its short
term funding
It had hundreds of thousands of transactions
outstanding with about 8,000 counterparties
Unwinding these transactions has been challenging for
both the Lehman liquidators and their counterparties
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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
To change the nature of a liability
To change the nature of an investment without
incurring the costs of selling one portfolio and
buying another
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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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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
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Class Exercise
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?
HINT consider different market conditions in 6 months
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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, ST K
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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 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
Less risk involved compared to forwards:
exchange traded means guarantee of
contract being honored
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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 (see list at end of book)
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Types of underlying assets in futures contracts
Commodities:
Pork bellies, live cattle, sugar, wool, copper, gold, oil.
Financial assets:
Stock indices, currencies and Treasury bonds
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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
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Class Exercise 2 Gold: An Arbitrage Opportunity?
Suppose that:
The spot price of gold is US$1,400
The 1-year quoted futures price of gold is US$1,500
The 1-year US$ interest rate is 5% per annum
Is there an arbitrage opportunity?
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Gold: Another Arbitrage Opportunity?
Suppose that:
- The spot price of gold is US$1,400 - The 1-year quoted futures 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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2. Gold: Another Arbitrage Opportunity?
Sell short gold at spot of $1,400
Invest $1,400 at 5% for 1 year = $1,470
Enter long into futures contract to buy back in 1 year at $1,400
After 1 year you gross $70 (note that we have ignored the borrowing cost of the short position in the gold)
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1. Oil: An Arbitrage Opportunity?
Suppose that:
- The spot price of oil is US$95 - The quoted 1-year futures price of
oil is US$125
- The 1-year US$ interest rate is 5% per annum
- The storage costs of oil are 2% per annum
Is there an arbitrage opportunity?
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The Forward Price of Oil
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 = 95, T = 1, and r =0.05 so that
F = 95(1+0.05) = $99.75
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1. Oil: An Arbitrage Opportunity?
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Borrow $95 at 5%, use to buy oil, then pay back loan in 1 year time $99.75
Storage cost 2% of $95 = $1.9
Sell 1 year futures $125
Total cost $99.75 + $1.9 = $101.65
Receive $125
Profit = $23.35
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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)
Traded both OTC and on exchange
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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
Most exchange traded are American options
Exchange traded equity options are usually an agreement to buy or sell 100 shares.
OTC options can have virtually any condition, which are agreed on by both counterparties
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Google Call Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25) Source: CBOE
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Strike
Price
Jul 17
2010 Bid
Jul 17
2010
Offer
Sep 18
2010 Bid
Sep 18
2010 Offer
Dec 18
2010 Bid
Dec 18
2010
Offer
460 43.30 44.00 51.90 53.90 63.40 64.80
480 28.60 29.00 39.70 40.40 50.80 52.30
500 17.00 17.40 28.30 29.30 40.60 41.30
520 9.00 9.30 19.10 19.90 31.40 32.00
540 4.20 4.40 12.70 13.00 23.10 24.00
560 1.75 2.10 7.40 8.40 16.80 17.70
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Google Put Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25); Source: CBOE
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Strike
Price
Jul 17
2010 Bid
Jul 17
2010
Offer
Sep 18
2010 Bid
Sep 18
2010 Offer
Dec 18
2010 Bid
Dec 18
2010
Offer
460 6.30 6.60 15.70 16.20 26.00 27.30
480 11.30 11.70 22.20 22.70 33.30 35.00
500 19.50 20.00 30.90 32.60 42.20 43.00
520 31.60 33.90 41.80 43.60 52.80 54.50
540 46.30 47.20 54.90 56.10 64.90 66.20
560 64.30 66.70 70.00 71.30 78.60 80.00
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Class exercise
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You want to buy one December call option on Google with strike of $520
Offer price is $32.00, this is for an option to buy one share, but exchange traded are on 100 shares
So you need $3,200 to buy contract
You now have the right to buy 100 Google shares at $520 each on December 18th 2010.
Consider 3 market scenarios after 6 months.
i) Google < $520 ii) Google =$530 iii) Google = $600
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Alternative strategy
Sell one September put option with strike price of $480
Price is $22.20 for 1 (remember you have to agree on 100 shares)
Cash inflow = $2,220 (Youve sold the put contract)
If Google share price remains above $480 by 18th September, you will earn $2,220, because the trader will not exercise the put option
If shares = $420 at maturity
You must buy 100 shares at $480 = $48,000, but they are only worth $420
= $3,780 total loss when accounting for the cash inflow from selling of put
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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 but not the
obligation
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Forward/futures payoffs
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Option payoffs
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What can derivatives be used for
Hedging
Speculating
Arbitrage
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Hedge example using forward
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
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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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Exporter can hedge against FX risks with a 3-month forward contract
3-month offer quote is 1.4415, in effect this fixes the prices to be paid to $14,415,000 = 10,000,000
The hedge can work in favour of the company or not.
Scenario 1: Ex rate is 1.3 on 24 Aug, company will wish it had not hedged because,
10,000,000 is only worth $13,000,000, but company is locked in at $14,415,000!
Scenario 2: Ex rate is 1.5, company is glad it has hedged otherwise it would have cost them $15,000,000 to deliver the 10m
Risk vs reward
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Hedge example using forward
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Hedge example using options
An investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1. The investor decides to hedge by buying 10 contracts
This investor is concerned about Microsoft share loosing value
Remember exchange traded options must be bought by the 100s..
10 contracts = put option on 1,000 shares
Total cost of hedge is $1,000
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Hedge example using options
Hedge costs $1,000 but guarantees sale of shares for $27.50
If share price falls below $27.50, the investor will exercise option, and sell shares for $27,500.
Taking into account option cost = $26,500 for investor
If share price stays above $27.50, option will not be exercised, but investor will still get back more than $26,500
If at $28.00, investor will get $27,000 (taking option cost into account.
Due to cost of the hedge, investor will always be $1,000 worse off if share price is above $27.50
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Value of Microsoft Shares with and without Hedging
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20,000
25,000
30,000
35,000
40,000
20 25 30 35 40
Value of Holding ($)
Stock Price ($)
No Hedging
Hedging
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Forwards/futures vs options
Forwards/futures neutralise risk by fixing the price paid or received for underlying asset
Option contracts provide insurance, because there is limited downfall, whilst allowing benefit from favourable price movements
Downside of option is the cost/premium
Forwards/futures have no upfront cost/premium
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Speculation Class exercise
An investor with $2,000 to invest feels that
a stock price will increase over the next 2
months. The current stock price is $20 and
the price of a 2-month call option with a
strike of 22.50 is $1
What are the strategies?
Consider
i) Buying shares ii) Buying call options
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Margins
A margin is cash or marketable securities deposited by
an investor with his or her broker
The balance in the margin account is adjusted to reflect
daily settlement
Margins minimize the possibility of a loss through a
default on a contract
Forwards are different, there are risks, counterparty may
not have financial resources to honor contract
Forwards are settled at maturity, whilst Futures are
settled daily
Futures are rarely held till 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 = $100, option life = 2 months
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30
20
10
0 -5
70 80 90 100
110 120 130
Profit ($)
Terminal
stock price ($)
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Short Call Profit from writing one European call option: option
price = $5, strike price = $100
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-30
-20
-10
0 5
70 80 90 100
110 120 130
Profit ($)
Terminal
stock price ($)
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Long Put Profit from buying a European put option: option
price = $7, strike price = $70
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30
20
10
0
-7 70 60 50 40 80 90 100
Profit ($)
Terminal
stock price ($)
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Short Put Profit from writing a European put option: option
price = $7, strike price = $70
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-30
-20
-10
7
0 70
60 50 40
80 90 100
Profit ($) Terminal
stock price ($)
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Payoffs from Options What is the Option Position in Each Case?
K = Strike price, ST = Price of asset at maturity
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Payoff Payoff
ST ST K
K
Payoff Payoff
ST ST K
K
Payoff = max(ST K, 0) Payoff = -max(ST K,
0)
Payoff = -max(K - ST, 0)
Payoff = max(K - ST, 0)
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Assets Underlying Exchange-Traded Options
Stocks
Foreign Currency
Stock Indices
Futures
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Specification of Exchange-Traded Options
Expiration date
Strike price
European or American
Call or Put (option class)
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Terminology
Moneyness : At-the-money option
In-the-money option
Out-of-the-money option
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Calls:
ATM Strike = Spot
ITM Strike < Spot
OTM Strike > Spot
Puts:
ATM Strike = Spot
ITM Strike > Spot
OTM Strike < Spot
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Google Call Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25) Source: CBOE
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Strike
Price
Jul 17
2010 Bid
Jul 17
2010
Offer
Sep 18
2010 Bid
Sep 18
2010 Offer
Dec 18
2010 Bid
Dec 18
2010
Offer
460 43.30 44.00 51.90 53.90 63.40 64.80
480 28.60 29.00 39.70 40.40 50.80 52.30
500 17.00 17.40 28.30 29.30 40.60 41.30
520 9.00 9.30 19.10 19.90 31.40 32.00
540 4.20 4.40 12.70 13.00 23.10 24.00
560 1.75 2.10 7.40 8.40 16.80 17.70
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Google Put Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25); See Table 1.3 page 9; Source: CBOE
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Strike
Price
Jul 17
2010 Bid
Jul 17
2010
Offer
Sep 18
2010 Bid
Sep 18
2010 Offer
Dec 18
2010 Bid
Dec 18
2010
Offer
460 6.30 6.60 15.70 16.20 26.00 27.30
480 11.30 11.70 22.20 22.70 33.30 35.00
500 19.50 20.00 30.90 32.60 42.20 43.00
520 31.60 33.90 41.80 43.60 52.80 54.50
540 46.30 47.20 54.90 56.10 64.90 66.20
560 64.30 66.70 70.00 71.30 78.60 80.00