Topic 1 intro to derivatives

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Topic 1Topic 1
Introduction To DerivativesIntroduction To Derivatives

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 This first lecture has four main goals:This first lecture has four main goals:
1.1. Introduce you to the notion of risk and the role of derivatives inIntroduce you to the notion of risk and the role of derivatives in
managing risk.managing risk.
 Discuss some of the general terms – such as short/long positions,Discuss some of the general terms – such as short/long positions,
bid-ask spread – from finance that we need.bid-ask spread – from finance that we need.
2.2. Introduce you to three major classes of derivative securities.Introduce you to three major classes of derivative securities.
 ForwardsForwards
 FuturesFutures
 OptionsOptions
3.3. Introduce you to the basic viewpoint needed to analyze theseIntroduce you to the basic viewpoint needed to analyze these
securities.securities.
4.4. Introduce you to the major traders of these instruments.Introduce you to the major traders of these instruments.
BasicsBasics

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BasicsBasics
 Finance is the study of risk.Finance is the study of risk.
 How to measure itHow to measure it
 How to reduce itHow to reduce it
 How to allocate itHow to allocate it
 All finance problems ultimately boil down to three mainAll finance problems ultimately boil down to three main
questions:questions:
 What are the cash flows, and when do they occur?What are the cash flows, and when do they occur?
 Who gets the cash flows?Who gets the cash flows?
 What is the appropriate discount rate for those cash flows?What is the appropriate discount rate for those cash flows?
 The difficulty, of course, is that normally none of thoseThe difficulty, of course, is that normally none of those
questions have an easy answer.questions have an easy answer.

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BasicsBasics
 As you know from other classes, we can generally classify risk asAs you know from other classes, we can generally classify risk as
being diversifiable or non-diversifiable:being diversifiable or non-diversifiable:
 Diversifiable – risk that is specific to a specific investment – i.e. the riskDiversifiable – risk that is specific to a specific investment – i.e. the risk
that a single company’s stock may go down (i.e. Enron). This isthat a single company’s stock may go down (i.e. Enron). This is
frequently calledfrequently called idiosyncratic risk.idiosyncratic risk.
 Non-diversifiable – risk that is common to all investing in general andNon-diversifiable – risk that is common to all investing in general and
that cannot be reduced – i.e. the risk that the entire stock market (orthat cannot be reduced – i.e. the risk that the entire stock market (or
bond market, or real estate market) will crash. This is frequently calledbond market, or real estate market) will crash. This is frequently called
systematic risksystematic risk ..
 The market “pays” you for bearing non-diversifiable risk only – notThe market “pays” you for bearing non-diversifiable risk only – not
for bearing diversifiable risk.for bearing diversifiable risk.
 In general the more non-diversifiable risk that you bear, the greater theIn general the more non-diversifiable risk that you bear, the greater the
expected return to your investment(s).expected return to your investment(s).
 Many investors fail to properly diversify, and as a result bear more riskMany investors fail to properly diversify, and as a result bear more risk
than they have to in order to earn a given level of expected return.than they have to in order to earn a given level of expected return.

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BasicsBasics
 In this sense, we can view the field of finance as beingIn this sense, we can view the field of finance as being
about two issues:about two issues:
 The elimination of diversifiable risk in portfolios;The elimination of diversifiable risk in portfolios;
 TheThe allocationallocation of systematic (non-diversifiable) risk to thoseof systematic (non-diversifiable) risk to those
members of society that are most willing to bear it.members of society that are most willing to bear it.
 Indeed, it is really this second function – the allocation ofIndeed, it is really this second function – the allocation of
systematic risk – that drives rates of return.systematic risk – that drives rates of return.
 The expected rate of return is the “price” that the market paysThe expected rate of return is the “price” that the market pays
investors for bearing systematic risk.investors for bearing systematic risk.

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BasicsBasics
 AA derivativederivative (or derivative security) is a financial(or derivative security) is a financial
instrument whose value depends upon the value ofinstrument whose value depends upon the value of
other, more basic, underlying variables.other, more basic, underlying variables.
 Some common examples include things such as stockSome common examples include things such as stock
options, futures, and forwards.options, futures, and forwards.
 It can also extend to something like a reimbursementIt can also extend to something like a reimbursement
program for college credit. Consider that if your firmprogram for college credit. Consider that if your firm
reimburses 100% of costs for an “A”, 75% of costs for areimburses 100% of costs for an “A”, 75% of costs for a
“B”, 50% for a “C” and 0% for anything less.“B”, 50% for a “C” and 0% for anything less.

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 Your “right” to claim this reimbursement, then is tied toYour “right” to claim this reimbursement, then is tied to
the grade you earn. The value of that reimbursementthe grade you earn. The value of that reimbursement
plan, therefore, isplan, therefore, is derivedderived from the grade you earn.from the grade you earn.
 We also say that the value isWe also say that the value is contingentcontingent upon the gradeupon the grade
you earn. Thus, your claim for reimbursement is ayou earn. Thus, your claim for reimbursement is a
“contingent” claim.“contingent” claim.
 The terms contingent claims and derivatives are usedThe terms contingent claims and derivatives are used
interchangeably.interchangeably.
BasicsBasics

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BasicsBasics
 So why do we have derivatives and derivatives markets?So why do we have derivatives and derivatives markets?
 Because they somehow allow investors to better control the levelBecause they somehow allow investors to better control the level
of risk that they bear.of risk that they bear.
 They can help eliminate idiosyncratic risk.They can help eliminate idiosyncratic risk.
 They can decrease or increase the level of systematic risk.They can decrease or increase the level of systematic risk.

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A First ExampleA First Example
 There is a neat example from the bond-world of aThere is a neat example from the bond-world of a
derivative that is used to move non-diversifiable risk fromderivative that is used to move non-diversifiable risk from
one set of investors to another set that are, presumably,one set of investors to another set that are, presumably,
more willing to bear that risk.more willing to bear that risk.
 Disney wanted to open a theme park in Tokyo, but didDisney wanted to open a theme park in Tokyo, but did
not want to have the shareholders bear the risk of annot want to have the shareholders bear the risk of an
earthquake destroying the park.earthquake destroying the park.
 They financed the park through the issuance of earthquakeThey financed the park through the issuance of earthquake
bonds.bonds.
 If an earthquake of at least 7.5 hit within 10 km of the park, theIf an earthquake of at least 7.5 hit within 10 km of the park, the
bonds did not have to be repaid, and there was a sliding scalebonds did not have to be repaid, and there was a sliding scale
for smaller quakes and for larger ones that were located furtherfor smaller quakes and for larger ones that were located further
away from the park.away from the park.

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 Normally this could have been handled in the insuranceNormally this could have been handled in the insurance
(and re-insurance) markets, but there would have been(and re-insurance) markets, but there would have been
transaction costs involved. By placing the risk directlytransaction costs involved. By placing the risk directly
upon the bondholders Disney was able to avoid thoseupon the bondholders Disney was able to avoid those
transactions costs.transactions costs.
 Presumably the bondholders of the Disney bonds are basicallyPresumably the bondholders of the Disney bonds are basically
the same investors that would have been holding the stock orthe same investors that would have been holding the stock or
bonds of the insurance/reinsurance companies.bonds of the insurance/reinsurance companies.
 Although the risk of earthquake is not diversifiable to the park, itAlthough the risk of earthquake is not diversifiable to the park, it
could be to Disney shareholders, so this does beg the questioncould be to Disney shareholders, so this does beg the question
of why buy the insurance at all.of why buy the insurance at all.
 This was not a “free” insurance. Disney paid LIBOR+310This was not a “free” insurance. Disney paid LIBOR+310
on the bond. If the earthquake provision was not it there,on the bond. If the earthquake provision was not it there,
they would have paid a lower rate.they would have paid a lower rate.

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 This example illustrates an interesting notion – thatThis example illustrates an interesting notion – that
insurance contracts (for property insurance) are reallyinsurance contracts (for property insurance) are really
derivatives!derivatives!
 They allow the owner of the asset to “sell” the insuredThey allow the owner of the asset to “sell” the insured
asset to the insurer in the event of a disaster.asset to the insurer in the event of a disaster.
 They are like put options (more on this later.)They are like put options (more on this later.)

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BasicsBasics
 Positions – In general if you are buying an asset – be it aPositions – In general if you are buying an asset – be it a
physical stock or bond, or the right to determine whetherphysical stock or bond, or the right to determine whether
or not you will acquire the asset in the future (such asor not you will acquire the asset in the future (such as
through an option or futures contract) you are said to bethrough an option or futures contract) you are said to be
“LONG” the instrument.“LONG” the instrument.
 If you are giving up the asset, or giving up the right toIf you are giving up the asset, or giving up the right to
determine whether or not you will own the asset in thedetermine whether or not you will own the asset in the
future, you are said to be “SHORT” the instrument.future, you are said to be “SHORT” the instrument.
 In the stock and bond markets, if you “short” an asset, it meansIn the stock and bond markets, if you “short” an asset, it means
that you borrow it, sell the asset, and then later buy it back.that you borrow it, sell the asset, and then later buy it back.
 In derivatives markets you generally do not have to borrow theIn derivatives markets you generally do not have to borrow the
instrument – you can simply take a position (such as writing aninstrument – you can simply take a position (such as writing an
option) that will require you to give up the asset or determinationoption) that will require you to give up the asset or determination
of ownership of the asset.of ownership of the asset.
 Usually in derivatives markets the “short” is just the negative ofUsually in derivatives markets the “short” is just the negative of
the “long” positionthe “long” position

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BasicsBasics
 Commissions – Virtually all transactions in the financialCommissions – Virtually all transactions in the financial
markets requires some form of commission payment.markets requires some form of commission payment.
 The size of the commission depends upon the relative positionThe size of the commission depends upon the relative position
of the trader: retail traders pay the most, institutional traders payof the trader: retail traders pay the most, institutional traders pay
less, market makers pay the least (but still pay to theless, market makers pay the least (but still pay to the
exchanges.)exchanges.)
 The larger the trade, the smaller the commission is inThe larger the trade, the smaller the commission is in
percentage terms.percentage terms.
 Bid-Ask spread – Depending upon whether you areBid-Ask spread – Depending upon whether you are
buying or selling an instrument, you will get differentbuying or selling an instrument, you will get different
prices. If you wish to sell, you will get a “BID” quote, andprices. If you wish to sell, you will get a “BID” quote, and
if you wish to buy you will get an “ASK” quote.if you wish to buy you will get an “ASK” quote.

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BasicsBasics
 The difference between the bid and the ask can varyThe difference between the bid and the ask can vary
depending upon whether you are a retail, institutional, ordepending upon whether you are a retail, institutional, or
broker trader; it can also vary if you are placing verybroker trader; it can also vary if you are placing very
large trades.large trades.
 In general, however, the bid-ask spread is relativelyIn general, however, the bid-ask spread is relatively
constant for a given customer/position.constant for a given customer/position.
 The spread is roughly a constant percentage of theThe spread is roughly a constant percentage of the
transaction, regardless of the scale – unlike thetransaction, regardless of the scale – unlike the
commission.commission.
 Especially in options trading, the bid-ask spread is aEspecially in options trading, the bid-ask spread is a
much bigger transaction cost than the commission.much bigger transaction cost than the commission.

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BasicsBasics
 Here are some example stock bid-ask spreads fromHere are some example stock bid-ask spreads from
8/22/2006:8/22/2006:
 IBM:IBM: Bid – 78.77Bid – 78.77 Ask – 78.79Ask – 78.79 0.025%0.025%
 ATT:ATT: Bid – 30.59Bid – 30.59 Ask – 30.60Ask – 30.60 0.033%0.033%
 Microsoft:Microsoft: Bid – 25.73Bid – 25.73 Ask – 25.74Ask – 25.74 0.039%0.039%
 Here are some example option bid-ask spreads (All withHere are some example option bid-ask spreads (All with
good volume)good volume)
 IBM Oct 85 Call:IBM Oct 85 Call: Bid – 2.05Bid – 2.05 Ask – 2.20Ask – 2.20 7.3171%7.3171%
 ATT Oct 15 Call:ATT Oct 15 Call: Bid – 0.50Bid – 0.50 Ask –0.55Ask –0.55 10.000%10.000%
 MSFT Oct 27.5 :MSFT Oct 27.5 : Bid – 0.70Bid – 0.70 Ask –0.80.Ask –0.80. 14.285%14.285%

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BasicsBasics
 The point of the preceding slide is to demonstrate thatThe point of the preceding slide is to demonstrate that
the bid-ask spread can be a huge factor in determiningthe bid-ask spread can be a huge factor in determining
the profitability of a trade.the profitability of a trade.
 Many of those option positions require at least a 10% priceMany of those option positions require at least a 10% price
movement before the trade is profitable.movement before the trade is profitable.
 Many “trading strategies” that you see people proposeMany “trading strategies” that you see people propose
(and that are frequently demonstrated using “real” data)(and that are frequently demonstrated using “real” data)
are based upon using the average of the bid-ask spread.are based upon using the average of the bid-ask spread.
They usually lose their effectiveness when the bid-askThey usually lose their effectiveness when the bid-ask
spread is considered.spread is considered.

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BasicsBasics
 Market Efficiency – We normally talk about financial markets asMarket Efficiency – We normally talk about financial markets as
being efficient information processors.being efficient information processors.
 Markets efficiently incorporate all publicly available information intoMarkets efficiently incorporate all publicly available information into
financial asset prices.financial asset prices.
 The mechanism through which this is done is by investors buying/sellingThe mechanism through which this is done is by investors buying/selling
based upon their discovery and analysis of new information.based upon their discovery and analysis of new information.
 The limiting factor in this is the transaction costs associated with theThe limiting factor in this is the transaction costs associated with the
market.market.
 For this reason, it is better to say that financial markets are efficientFor this reason, it is better to say that financial markets are efficient toto
within transactions costswithin transactions costs . Some financial economists say that. Some financial economists say that
financial markets are efficient to within the bid-ask spread.financial markets are efficient to within the bid-ask spread.
 Now, to a large degree for this class we can ignore the bid-ask spread,Now, to a large degree for this class we can ignore the bid-ask spread,
but there are some points where it will be particularly relevant, and webut there are some points where it will be particularly relevant, and we
will consider it then.will consider it then.

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BasicsBasics
 Before we begin to examine specific contracts, we needBefore we begin to examine specific contracts, we need
to consider two additional risks in the market:to consider two additional risks in the market:
 Credit risk – the risk that your trading partner might not honorCredit risk – the risk that your trading partner might not honor
their obligations.their obligations.
 Familiar risk to anybody that has traded on ebay!Familiar risk to anybody that has traded on ebay!
 Generally exchanges serve to mitigate this risk.Generally exchanges serve to mitigate this risk.
 Can also be mitigated by escrow accounts.Can also be mitigated by escrow accounts.
 Margin requirements are a form of escrow account.Margin requirements are a form of escrow account.
 Liquidity risk – the risk that when you need to buy or sell anLiquidity risk – the risk that when you need to buy or sell an
instrument you may not be able to find a counterparty.instrument you may not be able to find a counterparty.
 Can be very common for “outsiders” in commodities markets.Can be very common for “outsiders” in commodities markets.

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BasicsBasics
 So now we are going to begin examining the basicSo now we are going to begin examining the basic
instruments of derivatives. In particular we will look atinstruments of derivatives. In particular we will look at
(tonight):(tonight):
 ForwardsForwards
 FuturesFutures
 OptionsOptions
 The purpose of our discussion tonight is to simplyThe purpose of our discussion tonight is to simply
provide a basic understanding of the structure of theprovide a basic understanding of the structure of the
instruments and the basic reasons they might exist.instruments and the basic reasons they might exist.
 We will have a more in-detail examination of their properties,We will have a more in-detail examination of their properties,
and their pricing, in the weeks to come.and their pricing, in the weeks to come.

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AA forward contractforward contract is an agreement between two parties tois an agreement between two parties to
buy or sell an asset at a certain future time for a certainbuy or sell an asset at a certain future time for a certain
future price.future price.
 Forward contracts are normally not exchange traded.Forward contracts are normally not exchange traded.
 The party that agrees to buy the asset in the future is said toThe party that agrees to buy the asset in the future is said to
have thehave the longlong position.position.
 The party that agrees to sell the asset in the future is said toThe party that agrees to sell the asset in the future is said to
have thehave the shortshort position.position.
 The specified future date for the exchange is known as theThe specified future date for the exchange is known as the
delivery (delivery (maturitymaturity) date.) date.
Forward ContractsForward Contracts

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The specified price for the sale is known as theThe specified price for the sale is known as the deliverydelivery
price, we will denote this as K.price, we will denote this as K.
 Note that K is set such that at initiation of the contract the valueNote that K is set such that at initiation of the contract the value
of the forward contract is 0. Thus, by design, no cash changesof the forward contract is 0. Thus, by design, no cash changes
hands at time 0. The mechanics of how to do this we cover inhands at time 0. The mechanics of how to do this we cover in
later lectures.later lectures.
As time progresses the delivery price doesn’t change, butAs time progresses the delivery price doesn’t change, but
the current spot (market) rate does. Thus, the contractthe current spot (market) rate does. Thus, the contract
gains (or loses) value over time.gains (or loses) value over time.
 Consider the situation at the maturity date of the contract. If theConsider the situation at the maturity date of the contract. If the
spot price is higher than the delivery price, the long party canspot price is higher than the delivery price, the long party can
buy at K and immediately sell at the spot price Sbuy at K and immediately sell at the spot price STT, making a, making a
profit of (Sprofit of (STT-K), whereas the short position could have sold the-K), whereas the short position could have sold the
asset for Sasset for STT, but is obligated to sell for K, earning a profit, but is obligated to sell for K, earning a profit
(negative) of (K-S(negative) of (K-STT).).

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 Example:Example:
 Let’s say that you entered into a forward contract to buy wheatLet’s say that you entered into a forward contract to buy wheat
at $4.00/bushel, with delivery in December (thus K=$3.64.)at $4.00/bushel, with delivery in December (thus K=$3.64.)
 Let’s say that the delivery date was December 14 and that onLet’s say that the delivery date was December 14 and that on
December 14December 14thth
the market price of wheat is unlikely to be exactlythe market price of wheat is unlikely to be exactly
$4.00/bushel, but that is the price at which you have agreed (via$4.00/bushel, but that is the price at which you have agreed (via
the forward contract) to buy your wheat.the forward contract) to buy your wheat.
 If the market price is greater than $4.00/bushel, you are pleased,If the market price is greater than $4.00/bushel, you are pleased,
because you are able to buy an asset for less than its marketbecause you are able to buy an asset for less than its market
price.price.
 If, however, the market price is less than $4.00/bushel, you areIf, however, the market price is less than $4.00/bushel, you are
not pleased because you are paying more than the market pricenot pleased because you are paying more than the market price
for the wheat.for the wheat.
 Indeed, we can determine your net payoff to the trade byIndeed, we can determine your net payoff to the trade by
applying the formula: payoff = Sapplying the formula: payoff = STT – K, since you gain an asset– K, since you gain an asset
worth Sworth STT, but you have to pay $K for it., but you have to pay $K for it.
 We can graph the payoff function:We can graph the payoff function:

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Payoff to Futures Position on Wheat
Where the Delivery Price (K) is $4.00/Bushel
-4
-3
-2
-1
0
1
2
3
4
0 1 2 3 4 5 6 7 8
Wheat Market (Spot) Price, December 14
PayofftoForwards

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 Example:Example:
 In this example you were the long party, but what about theIn this example you were the long party, but what about the
short party?short party?
 They have agreed to sell wheat to you for $4.00/bushel onThey have agreed to sell wheat to you for $4.00/bushel on
December 14.December 14.
 Their payoff is positive if the market price of wheat is less thanTheir payoff is positive if the market price of wheat is less than
$4.00/bushel – they force you to pay more for the wheat than$4.00/bushel – they force you to pay more for the wheat than
they could sell it for on the open market.they could sell it for on the open market.
 Indeed, you could assume that what they do is buy it on the openIndeed, you could assume that what they do is buy it on the open
market and then immediately deliver it to you in the forwardmarket and then immediately deliver it to you in the forward
contract.contract.
 Their payoff is negative, however, if the market price of wheat isTheir payoff is negative, however, if the market price of wheat is
greater than $4.00/bushel.greater than $4.00/bushel.
 They could have sold the wheat for more than $4.00/bushel hadThey could have sold the wheat for more than $4.00/bushel had
they not agreed to sell it to you.they not agreed to sell it to you.
 So their payoff function is the mirror image of your payoffSo their payoff function is the mirror image of your payoff
function:function:

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Payoff to Short Futures Position on Wheat
Where the Delivery Price (K) is $4.00/Bushel
-4
-3
-2
-1
0
1
2
3
4
0 1 2 3 4 5 6 7 8
Wheat Market (Spot) Price, December 14
PayofftoForwards

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 Clearly the short position is just the mirror image of theClearly the short position is just the mirror image of the
long position, and, taken together the two positionslong position, and, taken together the two positions
cancel each other out:cancel each other out:

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Long and Short Positions in a Forward Contract
For Wheat at $4.00/Bushel
-4
-3
-2
-1
0
1
2
3
4
0 1 2 3 4 5 6 7 8
Wheat Price
Payoff
Long Position
Net
Position
Short Position

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Futures ContractsFutures Contracts
 A futures contract is similar to a forward contract in that it isA futures contract is similar to a forward contract in that it is
an agreement between two parties to buy or sell an assetan agreement between two parties to buy or sell an asset
at a certain time for a certain price. Futures, however, areat a certain time for a certain price. Futures, however, are
usually exchange traded and, to facilitate trading, areusually exchange traded and, to facilitate trading, are
usually standardized contracts. This results in moreusually standardized contracts. This results in more
institutional detail than is the case with forwards.institutional detail than is the case with forwards.
 The long and short party usually do not deal with eachThe long and short party usually do not deal with each
other directly or even know each other for that matter. Theother directly or even know each other for that matter. The
exchange acts as a clearinghouse. As far as the two sidesexchange acts as a clearinghouse. As far as the two sides
are concerned they are entering into contracts with theare concerned they are entering into contracts with the
exchange. In fact, the exchange guarantees performanceexchange. In fact, the exchange guarantees performance
of the contract regardless of whether the other party fails.of the contract regardless of whether the other party fails.

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 The largest futures exchanges are the Chicago Board ofThe largest futures exchanges are the Chicago Board of
Trade (CBOT) and the Chicago Mercantile ExchangeTrade (CBOT) and the Chicago Mercantile Exchange
(CME).(CME).
 Futures are traded on a wide range of commodities andFutures are traded on a wide range of commodities and
financial assets.financial assets.
 Usually an exact delivery date is not specified, but rather aUsually an exact delivery date is not specified, but rather a
delivery range is specified. The short position has thedelivery range is specified. The short position has the
option to choose when delivery is made. This is done tooption to choose when delivery is made. This is done to
accommodate physical delivery issues.accommodate physical delivery issues.
 Harvest dates vary from year to year, transportation schedulesHarvest dates vary from year to year, transportation schedules
change, etc.change, etc.

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 The exchange will usually place restrictions and conditionsThe exchange will usually place restrictions and conditions
on futures. These include:on futures. These include:
 Daily price (change) limits.Daily price (change) limits.
 For commodities, grade requirements.For commodities, grade requirements.
 Delivery method and place.Delivery method and place.
 How the contract is quoted.How the contract is quoted.
 Note however, that the basic payoffs are the same as for aNote however, that the basic payoffs are the same as for a
forward contract.forward contract.

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Options ContractsOptions Contracts
 Options on stocks were first traded in 1973. That wasOptions on stocks were first traded in 1973. That was
the year the famous Black-Scholes formula wasthe year the famous Black-Scholes formula was
published, along with Merton’s paper - a set ofpublished, along with Merton’s paper - a set of
academic papers that literally started an industry.academic papers that literally started an industry.
 Options exist on virtually anything. Tonight we areOptions exist on virtually anything. Tonight we are
going to focus on general options terminology forgoing to focus on general options terminology for
stocks. We will get into other types of options later instocks. We will get into other types of options later in
the class.the class.
 There are two basic types of options:There are two basic types of options:
 AA Call optionCall option is the right, but not the obligation, to buy theis the right, but not the obligation, to buy the
underlying asset by a certain date for a certain price.underlying asset by a certain date for a certain price.
 AA Put optionPut option is the right, but not the obligation, to sell theis the right, but not the obligation, to sell the
underlying asset by a certain date for a certain price.underlying asset by a certain date for a certain price.
 Note that unlike a forward or futures contract, the holder of theNote that unlike a forward or futures contract, the holder of the
options contract does not have to do anything - they have theoptions contract does not have to do anything - they have the
option to do it or not.option to do it or not.

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 The date when the option expires is known as theThe date when the option expires is known as the
exercise date, the expiration date, or the maturity date.exercise date, the expiration date, or the maturity date.
 The price at which the asset can be purchased or sold isThe price at which the asset can be purchased or sold is
known as the strike price.known as the strike price.
 If an option is said to be European, it means that theIf an option is said to be European, it means that the
holder of the option can buy or sell (depending on if it is aholder of the option can buy or sell (depending on if it is a
call or a put) only on the maturity date. If the option iscall or a put) only on the maturity date. If the option is
said to be an American style option, the holder cansaid to be an American style option, the holder can
exercise on any date up to and including the exerciseexercise on any date up to and including the exercise
date.date.
 An options contract is always costly to enter as the longAn options contract is always costly to enter as the long
party. The short party always is always paid to enter intoparty. The short party always is always paid to enter into
the contractthe contract
 Looking at the payoff diagrams you can see why…Looking at the payoff diagrams you can see why…

33
 Let’s say that you entered into a call option on IBMLet’s say that you entered into a call option on IBM
stock:stock:
 Today IBM is selling for roughly $78.80/share, so let’s say youToday IBM is selling for roughly $78.80/share, so let’s say you
entered into a call option that would let you buy IBM stock inentered into a call option that would let you buy IBM stock in
December at a price of $80/share.December at a price of $80/share.
 If in December the market price of IBM were greater than $80,If in December the market price of IBM were greater than $80,
you would exercise your option, and purchase the IBM share foryou would exercise your option, and purchase the IBM share for
$80.$80.
 If, in December IBM stock were selling for less than $80/share,If, in December IBM stock were selling for less than $80/share,
you could buy the stock for less by buying it in the open market,you could buy the stock for less by buying it in the open market,
so you would not exercise your option.so you would not exercise your option.
 Thus your payoff to the option is $0 if the IBM stock is less than $80Thus your payoff to the option is $0 if the IBM stock is less than $80
 It is (SIt is (STT-K) if IBM stock is worth more than $80-K) if IBM stock is worth more than $80
 Thus, your payoff diagram is:Thus, your payoff diagram is:

34
Long Call on IBM
with Strike Price (K) = $80
-20
0
20
40
60
80
0 20 40 60 80 100 120 140 160
IBM Terminal Stock Price
Payoff
K =
T

35
 What if you had the short position?What if you had the short position?
 Well, after you enter into the contract, you haveWell, after you enter into the contract, you have grantedgranted thethe
option to the long-party.option to the long-party.
 If they want to exercise the option, you have to do so.If they want to exercise the option, you have to do so.
 Of course, they will only exercise the option when it is in thereOf course, they will only exercise the option when it is in there
best interest to do so – that is, when the strike price is lower thanbest interest to do so – that is, when the strike price is lower than
the market price of the stock.the market price of the stock.
 So if the stock price is less than the strike price (SSo if the stock price is less than the strike price (STT<K), then the long<K), then the long
party will just buy the stock in the market, and so the option willparty will just buy the stock in the market, and so the option will
expire, and you will receive $0 at maturity.expire, and you will receive $0 at maturity.
 If the stock price is more than the strike price (SIf the stock price is more than the strike price (STT>K), however, then>K), however, then
the long party will exercise their option and you will have to sellthe long party will exercise their option and you will have to sell
them an asset that is worth Sthem an asset that is worth STT for $K.for $K.
 We can thus write your payoff as:We can thus write your payoff as:
payoff = min(0,Spayoff = min(0,STT-K),-K),
which has a graph that looks like:which has a graph that looks like:

36
Short Call Position on IBM Stock
-85
-63.75
-42.5
-21.25
0
21.25
0 20 40 60 80 100 120 140 160
Ending Stock Price
PayofftoShortPosition

37
 This is obviously the mirror image of the long position.This is obviously the mirror image of the long position.
 Notice, however, that at maturity, the short optionNotice, however, that at maturity, the short option
position can NEVER have a positive payout – the bestposition can NEVER have a positive payout – the best
that can happen is that they get $0.that can happen is that they get $0.
 This is why the short option party always demands an up-frontThis is why the short option party always demands an up-front
payment – it’s the only payment they are going to receive. Thispayment – it’s the only payment they are going to receive. This
payment is called the optionpayment is called the option premiumpremium or price.or price.
 Once again, the two positions “net out” to zero:Once again, the two positions “net out” to zero:

38
Long and Short Call Options on IBM
with Strike Prices of $80
-100
-80
-60
-40
-20
0
20
40
60
80
100
0 20 40 60 80 100 120 140 160
Ending Stock Price
Payoff
Long Call
Short Call
Net Position

39
 Recall that a put option grants the long party the right toRecall that a put option grants the long party the right to
sell the underlying at price K.sell the underlying at price K.
 Returning to our IBM example, if K=80, the long party willReturning to our IBM example, if K=80, the long party will
only elect to exercise the option if the price of the stockonly elect to exercise the option if the price of the stock
in the market is less than $80, otherwise they would justin the market is less than $80, otherwise they would just
sell it in the market.sell it in the market.
 The payoff to the holder of the long put position,The payoff to the holder of the long put position,
therefore is simplytherefore is simply
payoff = max(0, K-Spayoff = max(0, K-STT))

40
Payoff to Long Put Option on IBM
with Strike Price of $80
-10
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120 140 160
Ending Stock Price
Payoff

41
 The short position again has granted the option to theThe short position again has granted the option to the
long position. The short has to buy the stock at price K,long position. The short has to buy the stock at price K,
when the long party wants them to do so. Of course thewhen the long party wants them to do so. Of course the
long party will only do this when the stock price is lesslong party will only do this when the stock price is less
than the strike price.than the strike price.
 Thus, the payoff function for the short put position is:Thus, the payoff function for the short put position is:
payoff = min(0, Spayoff = min(0, STT-K)-K)
 And the payoff diagram looks like:And the payoff diagram looks like:

42
Short Put Option on IBM
with Strike Price of $80
-85
-63.75
-42.5
-21.25
0
0 20 40 60 80 100 120 140 160
Ending Stock Price
Payoff

43
 Since the short put party can never receive a positiveSince the short put party can never receive a positive
payout at maturity, they demand a payment up-front frompayout at maturity, they demand a payment up-front from
the long party – that is, they demand that the long partythe long party – that is, they demand that the long party
pay apay a premiumpremium to induce them to enter into theto induce them to enter into the
contract.contract.
 Once again, the short and long positions net out to zero:Once again, the short and long positions net out to zero:
when one party wins, the other loses.when one party wins, the other loses.

44
Long and Short Put Options on IBM
with Strike Prices of $80
-100
-80
-60
-40
-20
0
20
40
60
80
100
0 20 40 60 80 100 120 140 160
Ending Stock Price
Payoff
Long Position
Short Position
Net Position

45
 The standard options contract is for 100 units of theThe standard options contract is for 100 units of the
underlying. Thus if the option is selling for $5, youunderlying. Thus if the option is selling for $5, you
would have to enter into a contract for 100 of thewould have to enter into a contract for 100 of the
underlying stock, and thus the cost of entering would beunderlying stock, and thus the cost of entering would be
$500.$500.
 For a European call, the payoff to the option is:For a European call, the payoff to the option is:
 Max(0,SMax(0,STT-K)-K)
 For a European put it isFor a European put it is
 Max(0,K-SMax(0,K-STT))
 The short positions are just the negative of these:The short positions are just the negative of these:
 Short call: -Max(0,SShort call: -Max(0,STT-K) = Min(0,K-S-K) = Min(0,K-STT))
 Short put: -Max(0,K-SShort put: -Max(0,K-STT)) = Min(0,S= Min(0,STT-K)-K)

46
 Traders frequently refer to an option as being “in theTraders frequently refer to an option as being “in the
money”, “out of the money” or “at the money”.money”, “out of the money” or “at the money”.
 An “in the money” option means one where the price of theAn “in the money” option means one where the price of the
underlying is such that if the option were exercised immediately,underlying is such that if the option were exercised immediately,
the option holder would receive a payout.the option holder would receive a payout.
 For a call option this means that SFor a call option this means that Stt>K>K
 For a put option this means that SFor a put option this means that Stt<K<K
 An “at the money” option means one where the strike andAn “at the money” option means one where the strike and
exercise prices are the same.exercise prices are the same.
 An “out of the money” option means one where the price of theAn “out of the money” option means one where the price of the
underlying is such that if the option were exercised immediately,underlying is such that if the option were exercised immediately,
the option holder would NOT receive a payout.the option holder would NOT receive a payout.
 For a call option this means that SFor a call option this means that Stt<K<K
 For a put option this means that SFor a put option this means that Stt>K.>K.

47
Long Call on IBM
-20
0
20
40
60
80
0 20 40 60 80 100 120 140 160
IBM Terminal Stock Price
Payoff
K =
T
Out of the money In the money
At the money

48
 One interesting notion is to look at the payoff from justOne interesting notion is to look at the payoff from just
owning the stock – its value is simply the value of theowning the stock – its value is simply the value of the
stock:stock:

49
Payout Diagram for a Long Position in IBM Stock
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160
Ending Stock Price
Payoff

50
 What is interesting is if we compare the payout from aWhat is interesting is if we compare the payout from a
portfolio containing a short put and a long call with theportfolio containing a short put and a long call with the
payout from just owning the stock:payout from just owning the stock:

51
-100
-50
0
50
100
150
200
0 20 40 60 80 100 120 140 160
Ending Stock Price
Payoff
Long Call
Short Put
Stock

52
 Notice how the payoff to the options portfolio has theNotice how the payoff to the options portfolio has the
same shape and slope as the stock position – just offsetsame shape and slope as the stock position – just offset
by some amount?by some amount?
 This is hinting at one of the most important relationshipsThis is hinting at one of the most important relationships
in options theory – Put-Call parity.in options theory – Put-Call parity.
 It may be easier to see this if we examine the aggregateIt may be easier to see this if we examine the aggregate
position of the options portfolio:position of the options portfolio:

53
-100
-50
0
50
100
150
200
0 20 40 60 80 100 120 140 160
Ending Stock Price
Payoff

54
 We will come back to put-call parity in a few weeks, but itWe will come back to put-call parity in a few weeks, but it
is well worth keeping this diagram in mind.is well worth keeping this diagram in mind.
 So who trades options contracts? Generally there areSo who trades options contracts? Generally there are
three types of options traders:three types of options traders:
 HedgersHedgers - these are firms that face a business risk. They wish- these are firms that face a business risk. They wish
to get rid of this uncertainty using a derivative. For example, anto get rid of this uncertainty using a derivative. For example, an
airline might use a derivatives contract to hedge the risk that jetairline might use a derivatives contract to hedge the risk that jet
fuel prices might change. fuel prices might change.
 SpeculatorsSpeculators - They want to take a bet (position) in the market- They want to take a bet (position) in the market
and simply want to be in place to capture expected up or downand simply want to be in place to capture expected up or down
movements.movements.
 ArbitrageursArbitrageurs - They are looking for imperfections in the capital- They are looking for imperfections in the capital
market.market.

55
Financial EngineeringFinancial Engineering
 When we start examining the actual pricing of derivativesWhen we start examining the actual pricing of derivatives
(next week), one of the fundamental ideas that we will(next week), one of the fundamental ideas that we will
use is the “law of one price”.use is the “law of one price”.
 Basically this says that if two portfolios offer the sameBasically this says that if two portfolios offer the same
cash flows in all potential states of the world, then thecash flows in all potential states of the world, then the
two portfolios must sell for the same price in the market –two portfolios must sell for the same price in the market –
regardless of the instruments contained in the portfolios.regardless of the instruments contained in the portfolios.
 This is only true to “within transactions costs”, i.e. the bid-askThis is only true to “within transactions costs”, i.e. the bid-ask
spread on each individual instrument.spread on each individual instrument.
 Sometimes one portfolio will have such lower transactions costsSometimes one portfolio will have such lower transactions costs
that the law will only approximately hold.that the law will only approximately hold.

56
 Financial engineering is the notion that you can use aFinancial engineering is the notion that you can use a
combination of assets and financial derivatives tocombination of assets and financial derivatives to
construct cash flow streams that would otherwise beconstruct cash flow streams that would otherwise be
difficult or impossible to obtain.difficult or impossible to obtain.
 Financial engineering can be used to “break apart” a setFinancial engineering can be used to “break apart” a set
of cash flows into component pieces that each haveof cash flows into component pieces that each have
different risks and that can be sold to different investors.different risks and that can be sold to different investors.
 Collateralized Bond Obligations do this for “junk” bonds.Collateralized Bond Obligations do this for “junk” bonds.
 Collateralized Mortgage Obligations do this for residentialCollateralized Mortgage Obligations do this for residential
mortgages.mortgages.
 Financial engineering can also be used to create cashFinancial engineering can also be used to create cash
flows streams that would otherwise be difficult to obtain.flows streams that would otherwise be difficult to obtain.

57
 The Schwab/First Union equity-linked CD is a goodThe Schwab/First Union equity-linked CD is a good
example of financial engineering.example of financial engineering.
 When it was issued (in 1999), the stock market was (andWhen it was issued (in 1999), the stock market was (and
had been) incredibly “hot” for several years.had been) incredibly “hot” for several years.
 Many investors wanted to be in the market, but did not want toMany investors wanted to be in the market, but did not want to
risk the market going down in value.risk the market going down in value.
 The equity-linked CD was designed to meet this need.The equity-linked CD was designed to meet this need.
 As we will demonstrate, an investor could “roll their own” versionAs we will demonstrate, an investor could “roll their own” version
of this, but in doing so would have incurred significantof this, but in doing so would have incurred significant
transaction costs.transaction costs.
 Plus, many small investors (to whom this was targeted) probablyPlus, many small investors (to whom this was targeted) probably
could not get approval to trade options.could not get approval to trade options.

58
 The Contract:The Contract:
 An investor buys the CD (Certificate of Deposit) today, and then earnsAn investor buys the CD (Certificate of Deposit) today, and then earns
70% of the simple rate of return on S&P 500 index over the next 5.570% of the simple rate of return on S&P 500 index over the next 5.5
years.years.
 If the S&P index ended up below the initial index level (so that theIf the S&P index ended up below the initial index level (so that the
appreciation was negative), then the investor received their full initialappreciation was negative), then the investor received their full initial
investment back, but nothing else.investment back, but nothing else.
 Thus, the payoff to the CD was simply:Thus, the payoff to the CD was simply:
 So let’s say that you invested $10,000, and that in June of 1999 theSo let’s say that you invested $10,000, and that in June of 1999 the
index was 1300 (so that you were, in essence, buying $10,000/1,300 orindex was 1300 (so that you were, in essence, buying $10,000/1,300 or
7.69 units of the index).7.69 units of the index).
5.5
0
* 1 max 0, 1Maturity
Index
CD Investment
Index
  
= + − ÷  ÷
  

59
 In 5.5 years your payoff will be based upon the indexIn 5.5 years your payoff will be based upon the index
level. Potential index levels and payoffs include:level. Potential index levels and payoffs include:
IndexIndex Simple Rate of ReturnSimple Rate of Return Cash ReceivedCash Received
10001000 - 23.07%- 23.07% $10,000$10,000
12001200 - 7.69%- 7.69% $10,000$10,000
13001300 0.00%0.00% $10,000$10,000
14001400 7.69%7.69% $10,538$10,538
15001500 15.38%15.38% $11,076$11,076
20002000 53.85%53.85% $13,769$13,769
(Note that on 12/30/2004 the S&P 500 was at 1211.92!)(Note that on 12/30/2004 the S&P 500 was at 1211.92!)
 The following chart demonstrates the payouts.The following chart demonstrates the payouts.

60
Payoff to Equity Linked Swap
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0 500 1000 1500 2000 2500
S&P 500 Level
Payoff

61
 Now, the first thing about that chart that you shouldNow, the first thing about that chart that you should
notice is that it looks an awful lot like the shape of a callnotice is that it looks an awful lot like the shape of a call
option, although the slope of the upward-sloping part isoption, although the slope of the upward-sloping part is
not as steep.not as steep.
 This is our first indication that we may be able toThis is our first indication that we may be able to
decompose this into two simpler securities.decompose this into two simpler securities.
 Indeed, one way of decomposing this security would beIndeed, one way of decomposing this security would be
to assume that we bought a bond that paid $10,000 atto assume that we bought a bond that paid $10,000 at
time 5.5, and that we bought 5.38 call options with atime 5.5, and that we bought 5.38 call options with a
strike of 1300 (70% of 10,000/1300.)strike of 1300 (70% of 10,000/1300.)
 The next graph demonstrates this position’s payoff.The next graph demonstrates this position’s payoff.

62
Bond Plus Call Payoff
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0 500 1000 1500 2000 2500 3000
Index Value
Payoff
Option Payoff
Bond Payoff
Net

63
 This position is ALSO identical to a position consisting of:This position is ALSO identical to a position consisting of:
 $10,000/1300 = 7.692 units of the index.$10,000/1300 = 7.692 units of the index.
 $10,000/1300 = 7.692 put options on the index (K=1300)$10,000/1300 = 7.692 put options on the index (K=1300)
 (-(1-.7)*$10,000/1300 = -2.30769) CALL options on the index.(-(1-.7)*$10,000/1300 = -2.30769) CALL options on the index.
 The reason for the short call options is because the CDThe reason for the short call options is because the CD
only gives us 70% of the return on the index, so we haveonly gives us 70% of the return on the index, so we have
to sell back some of that return via the call option (noteto sell back some of that return via the call option (note
that we will earn a premium for this.)that we will earn a premium for this.)
 The following chart shows this:The following chart shows this:

64
Long Index, Long Put, Short Call
-5000
0
5000
10000
15000
20000
25000
0 500 1000 1500 2000 2500 3000
Index
Payoff
Index Payoff
Put Position
Call Position
Net

65
 Now, all three of theseNow, all three of these shouldshould sell for the same price – but theresell for the same price – but there
will be some differences because of transactions costs.will be some differences because of transactions costs.
 Really, this is why the Schwab equity-linked CD can work: investorsReally, this is why the Schwab equity-linked CD can work: investors
(retail investors) are willing to turn to the “prepackaged” asset to(retail investors) are willing to turn to the “prepackaged” asset to
avoid transaction costs (and to avoid timing difficulties with unwindingavoid transaction costs (and to avoid timing difficulties with unwinding
their position.)their position.)
 Let’s just think of this as a bond and .7 long call options for aLet’s just think of this as a bond and .7 long call options for a
moment.moment.
 Clearly the call cannot be free, since the investor holds this optionClearly the call cannot be free, since the investor holds this option
they must pay something for it. How much do they pay?they must pay something for it. How much do they pay?
 The interest that they could have earned on this money had theyThe interest that they could have earned on this money had they
invested in a traditional CD.invested in a traditional CD.
 At that time 5.5 year CDs were yielding 6%, so the investor “givesAt that time 5.5 year CDs were yielding 6%, so the investor “gives
up” $3,777 dollars in year 5.5 dollars.up” $3,777 dollars in year 5.5 dollars.
5.5
($10,000*1.06 ) 10,000 3,777− =

66
 The equity-linked CD is just one example of financialThe equity-linked CD is just one example of financial
engineering – the notion that investors are really justengineering – the notion that investors are really just
purchasing potential future cash flows and that any twopurchasing potential future cash flows and that any two
sets of identical potential future cash flows must sell forsets of identical potential future cash flows must sell for
the same price.the same price.
 This has led to a real revolution in finance, and we willThis has led to a real revolution in finance, and we will
discuss this idea throughout the semester.discuss this idea throughout the semester.
 We will return to options pricing later in the semester.We will return to options pricing later in the semester.
Next, we turn our attention to the futures/forwardsNext, we turn our attention to the futures/forwards
markets and pricing.markets and pricing.

Topic 1 intro to derivatives

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