1. 1 Topic 1 Introduction To Derivatives

2. 2 This lecture has four main goals: This lecture has four main goals: 1. Introduce you to the notion of risk and the role of derivatives in managing risk. Discuss some of the general terms – such as short/long positions, bid-ask spread – from finance that we need. Discuss some of the general terms – such as short/long positions, bid-ask spread – from finance that we need. 2. Introduce you to three major classes of derivative securities. Forwards Forwards Futures Futures Options Options 3. Introduce you to the basic viewpoint needed to analyze these securities. 4. Introduce you to the major traders of these instruments. Basics

3. 3 Basics Finance is the study of risk. Finance is the study of risk. How to measure it How to measure it How to reduce it How to reduce it How to allocate it How to allocate it All finance problems ultimately boil down to three main questions: All finance problems ultimately boil down to three main 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 those questions have an easy answer. The difficulty, of course, is that normally none of those questions have an easy answer.

4. 4 Basics As you may know from other classes, we can generally classify risk as being diversifiable or non-diversifiable: As you may know from other classes, we can generally classify risk as being diversifiable or non-diversifiable: Diversifiable – 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 is frequently called idiosyncratic risk. Diversifiable – 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 is frequently called idiosyncratic risk. Non-diversifiable – risk that is common to all investing in general and that cannot be reduced – i.e. the risk that the entire stock market (or bond market, or real estate market) will crash. This is frequently called systematic risk. Non-diversifiable – risk that is common to all investing in general and that cannot be reduced – i.e. the risk that the entire stock market (or bond market, or real estate market) will crash. This is frequently called systematic risk. The market “pays” you for bearing non-diversifiable risk only – not for bearing diversifiable risk. The market “pays” you for bearing non-diversifiable risk only – not for bearing diversifiable risk. In general the more non-diversifiable risk that you bear, the greater the expected return to your investment(s). In general the more non-diversifiable risk that you bear, the greater the expected return to your investment(s). Many 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. Many 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.

5. 5 Basics In this sense, we can view the field of finance as being about two issues: In this sense, we can view the field of finance as being about two issues: The elimination of diversifiable risk in portfolios; The elimination of diversifiable risk in portfolios; The allocation of systematic (non-diversifiable) risk to those members of society that are most willing to bear it. The allocation of systematic (non-diversifiable) risk to those members of society that are most willing to bear it. Indeed, it is really this second function – the allocation of systematic risk – that drives rates of return. Indeed, it is really this second function – the allocation of systematic risk – that drives rates of return. The expected rate of return is the “price” that the market pays investors for bearing systematic risk. The expected rate of return is the “price” that the market pays investors for bearing systematic risk.

6. 6 Basics A derivative (or derivative security) is a financial instrument whose value depends upon the value of other, more basic, underlying variables. A derivative (or derivative security) is a financial instrument whose value depends upon the value of other, more basic, underlying variables. Some common examples include things such as stock options, futures, and forwards. Some common examples include things such as stock options, futures, and forwards. It can also extend to something like a reimbursement program for college credit. Consider that if your firm reimburses 100% of costs for an “A”, 75% of costs for a “B”, 50% for a “C” and 0% for anything less. It can also extend to something like a reimbursement program for college credit. Consider that if your firm reimburses 100% of costs for an “A”, 75% of costs for a “B”, 50% for a “C” and 0% for anything less.

7. 7 Your “right” to claim this reimbursement, then is tied to the grade you earn. The value of that reimbursement plan, therefore, is derived from the grade you earn. Your “right” to claim this reimbursement, then is tied to the grade you earn. The value of that reimbursement plan, therefore, is derived from the grade you earn. We also say that the value is contingent upon the grade you earn. Thus, your claim for reimbursement is a “contingent” claim. We also say that the value is contingent upon the grade you earn. Thus, your claim for reimbursement is a “contingent” claim. The terms contingent claims and derivatives are used interchangeably. The terms contingent claims and derivatives are used interchangeably. Basics

8. 8 Basics 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 level of risk that they bear. Because they somehow allow investors to better control the level 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.

9. 9 A First Example There is a neat example from the bond-world of a derivative that is used to move non-diversifiable risk from one set of investors to another set that are, presumably, more willing to bear that risk. There is a neat example from the bond-world of a derivative that is used to move non-diversifiable risk from one set of investors to another set that are, presumably, more willing to bear that risk. Disney wanted to open a theme park in Tokyo, but did not want to have the shareholders bear the risk of an earthquake destroying the park. Disney wanted to open a theme park in Tokyo, but did not want to have the shareholders bear the risk of an earthquake destroying the park. They financed the park through the issuance of earthquake bonds. They financed the park through the issuance of earthquake bonds. If 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 scale for smaller quakes and for larger ones that were located further away from the park. If 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 scale for smaller quakes and for larger ones that were located further away from the park.

10. 10 A First Example Normally this could have been handled in the insurance (and re-insurance) markets, but there would have been transaction costs involved. By placing the risk directly upon the bondholders Disney was able to avoid those transactions costs. Normally this could have been handled in the insurance (and re-insurance) markets, but there would have been transaction costs involved. By placing the risk directly upon the bondholders Disney was able to avoid those transactions costs. Presumably the bondholders of the Disney bonds are basically the same investors that would have been holding the stock or bonds of the insurance/reinsurance companies. Presumably the bondholders of the Disney bonds are basically the same investors that would have been holding the stock or bonds of the insurance/reinsurance companies. Although the risk of earthquake is not diversifiable to the park, it could be to Disney shareholders, so this does beg the question of why buy the insurance at all. Although the risk of earthquake is not diversifiable to the park, it could be to Disney shareholders, so this does beg the question of why buy the insurance at all. This was not a “free” insurance. Disney paid LIBOR+310 on the bond. If the earthquake provision was not it there, they would have paid a lower rate. This was not a “free” insurance. Disney paid LIBOR+310 on the bond. If the earthquake provision was not it there, they would have paid a lower rate.

11. 11 A First Example This example illustrates an interesting notion – that insurance contracts (for property insurance) are really derivatives! This example illustrates an interesting notion – that insurance contracts (for property insurance) are really derivatives! They allow the owner of the asset to “sell” the insured asset to the insurer in the event of a disaster. They allow the owner of the asset to “sell” the insured 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.)

12. 12 Basics Positions – In general if you are buying an asset – be it a physical stock or bond, or the right to determine whether or not you will acquire the asset in the future (such as through an option or futures contract) you are said to be “LONG” the instrument. Positions – In general if you are buying an asset – be it a physical stock or bond, or the right to determine whether or not you will acquire the asset in the future (such as through an option or futures contract) you are said to be “LONG” the instrument. If you are giving up the asset, or giving up the right to determine whether or not you will own the asset in the future, you are said to be “SHORT” the instrument. If you are giving up the asset, or giving up the right to determine whether or not you will own the asset in the future, you are said to be “SHORT” the instrument. In 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. In 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. In derivatives markets you generally do not have to borrow the instrument – you can simply take a position (such as writing an option) that will require you to give up the asset or determination of ownership of the asset. In derivatives markets you generally do not have to borrow the instrument – you can simply take a position (such as writing an option) that will require you to give up the asset or determination of ownership of the asset. Usually in derivatives markets the “short” is just the negative of the “long” position Usually in derivatives markets the “short” is just the negative of the “long” position

13. 13 Basics Commissions – Virtually all transactions in the financial markets requires some form of commission payment. Commissions – Virtually all transactions in the financial markets requires some form of commission payment. The size of the commission depends upon the relative position of the trader: retail traders pay the most, institutional traders pay less, market makers pay the least (but still pay to the exchanges.) The size of the commission depends upon the relative position of the trader: retail traders pay the most, institutional traders pay less, market makers pay the least (but still pay to the exchanges.) The larger the trade, the smaller the commission is in percentage terms. The larger the trade, the smaller the commission is in percentage terms. Bid-Ask spread – Depending upon whether you are buying or selling an instrument, you will get different prices. If you wish to sell, you will get a “BID” quote, and if you wish to buy you will get an “ASK” quote. Bid-Ask spread – Depending upon whether you are buying or selling an instrument, you will get different prices. If you wish to sell, you will get a “BID” quote, and if you wish to buy you will get an “ASK” quote.

14. 14 Basics The difference between the bid and the ask can vary depending upon whether you are a retail, institutional, or broker trader; it can also vary if you are placing very large trades. The difference between the bid and the ask can vary depending upon whether you are a retail, institutional, or broker trader; it can also vary if you are placing very large trades. In general, however, the bid-ask spread is relatively constant for a given customer/position. In general, however, the bid-ask spread is relatively constant for a given customer/position. The spread is roughly a constant percentage of the transaction, regardless of the scale – unlike the commission. The spread is roughly a constant percentage of the transaction, regardless of the scale – unlike the commission. Especially in options trading, the bid-ask spread is a much bigger transaction cost than the commission. Especially in options trading, the bid-ask spread is a much bigger transaction cost than the commission.

15. 15 Basics Here are some example stock bid-ask spreads from 8/22/2006: Here are some example stock bid-ask spreads from 8/22/2006: IBM: Bid – 78.77 Ask – 78.790.025% IBM: Bid – 78.77 Ask – 78.790.025% ATT: Bid – 30.59Ask – 30.600.033% ATT: Bid – 30.59Ask – 30.600.033% Microsoft:Bid – 25.73 Ask – 25.740.039% Microsoft:Bid – 25.73 Ask – 25.740.039% Here are some example option bid-ask spreads (All with good volume) Here are some example option bid-ask spreads (All with good volume) IBM Oct 85 Call: Bid – 2.05Ask – 2.207.3171% IBM Oct 85 Call: Bid – 2.05Ask – 2.207.3171% ATT Oct 15 Call:Bid – 0.50Ask –0.5510.000% ATT Oct 15 Call:Bid – 0.50Ask –0.5510.000% MSFT Oct 27.5 : Bid – 0.70Ask –0.80.14.285% MSFT Oct 27.5 : Bid – 0.70Ask –0.80.14.285%

16. 16 Basics The point of the preceding slide is to demonstrate that the bid-ask spread can be a huge factor in determining the profitability of a trade. The point of the preceding slide is to demonstrate that the bid-ask spread can be a huge factor in determining the profitability of a trade. Many of those option positions require at least a 10% price movement before the trade is profitable. Many of those option positions require at least a 10% price movement before the trade is profitable. Many “trading strategies” that you see people propose (and that are frequently demonstrated using “real” data) are based upon using the average of the bid-ask spread. They usually lose their effectiveness when the bid-ask spread is considered. Many “trading strategies” that you see people propose (and that are frequently demonstrated using “real” data) are based upon using the average of the bid-ask spread. They usually lose their effectiveness when the bid-ask spread is considered.

17. 17 Basics Market Efficiency – We normally talk about financial markets as being efficient information processors. Market Efficiency – We normally talk about financial markets as being efficient information processors. Markets efficiently incorporate all publicly available information into financial asset prices. Markets efficiently incorporate all publicly available information into financial asset prices. The mechanism through which this is done is by investors buying/selling based upon their discovery and analysis of new information. The mechanism through which this is done is by investors buying/selling based upon their discovery and analysis of new information. The limiting factor in this is the transaction costs associated with the market. The limiting factor in this is the transaction costs associated with the market. For this reason, it is better to say that financial markets are efficient to within transactions costs. Some financial economists say that financial markets are efficient to within the bid-ask spread. For this reason, it is better to say that financial markets are efficient to within transactions costs. Some financial economists say that 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, but there are some points where it will be particularly relevant, and we will consider it then. 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 we will consider it then.

18. 18 Basics Before we begin to examine specific contracts, we need to consider two additional risks in the market: Before we begin to examine specific contracts, we need to consider two additional risks in the market: Credit risk – the risk that your trading partner might not honor their obligations. Credit risk – the risk that your trading partner might not honor 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 an instrument you may not be able to find a counterparty. Liquidity risk – the risk that when you need to buy or sell an 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.

19. 19 Basics So now we are going to begin examining the basic instruments of derivatives. In particular we will look at (tonight): So now we are going to begin examining the basic instruments of derivatives. In particular we will look at (tonight): Forwards Forwards Futures Futures Options Options The purpose of our discussion today is to simply provide a basic understanding of the structure of the instruments and the basic reasons they might exist. The purpose of our discussion today is to simply provide a basic understanding of the structure of the instruments and the basic reasons they might exist.

20. 20 A forward contract is an agreement between two parties to buy or sell an asset at a certain future time for a certain 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 to have the long position. The party that agrees to buy the asset in the future is said to have the long position. The party that agrees to sell the asset in the future is said to have the short position. The party that agrees to sell the asset in the future is said to have the short position. The specified future date for the exchange is known as the delivery (maturity) date. The specified future date for the exchange is known as the delivery (maturity) date. Forward Contracts

21. 21 The specified price for the sale is known as the delivery price, we will denote this as K. Note that K is set such that at initiation of the contract the value of the forward contract is 0. Thus, by design, no cash changes hands at time 0. The mechanics of how to do this we cover in later lectures. Note that K is set such that at initiation of the contract the value of the forward contract is 0. Thus, by design, no cash changes hands at time 0. The mechanics of how to do this we cover in later lectures. As time progresses the delivery price doesn’t change, but the current spot (market) rate does. Thus, the contract gains (or loses) value over time. Consider the situation at the maturity date of the contract. If the spot price is higher than the delivery price, the long party can buy at K and immediately sell at the spot price S T, making a profit of (S T -K), whereas the short position could have sold the asset for S T, but is obligated to sell for K, earning a profit (negative) of (K-S T ). Consider the situation at the maturity date of the contract. If the spot price is higher than the delivery price, the long party can buy at K and immediately sell at the spot price S T, making a profit of (S T -K), whereas the short position could have sold the asset for S T, but is obligated to sell for K, earning a profit (negative) of (K-S T ). Forward Contracts

22. 22 Example: Example: Let’s say that you entered into a forward contract to buy wheat at $4.00/bushel, with delivery in December (thus K=$3.64.) Let’s say that you entered into a forward contract to buy wheat at $4.00/bushel, with delivery in December (thus K=$3.64.) Let’s say that the delivery date was December 14 and that on December 14 th the market price of wheat is unlikely to be exactly $4.00/bushel, but that is the price at which you have agreed (via the forward contract) to buy your wheat. Let’s say that the delivery date was December 14 and that on December 14 th the market price of wheat is unlikely to be exactly $4.00/bushel, but that is the price at which you have agreed (via the forward contract) to buy your wheat. 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 market price. 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 market price. If, however, the market price is less than $4.00/bushel, you are not pleased because you are paying more than the market price for the wheat. If, however, the market price is less than $4.00/bushel, you are not pleased because you are paying more than the market price for the wheat. Indeed, we can determine your net payoff to the trade by applying the formula: payoff = S T – K, since you gain an asset worth S T, but you have to pay $K for it. Indeed, we can determine your net payoff to the trade by applying the formula: payoff = S T – K, since you gain an asset worth S T, but you have to pay $K for it. We can graph the payoff function: We can graph the payoff function: Forward Contracts

23. 23 Forward Contracts

24. 24 Example: Example: In this example you were the long party, but what about the short party? In this example you were the long party, but what about the short party? They have agreed to sell wheat to you for $4.00/bushel on December 14. They have agreed to sell wheat to you for $4.00/bushel on December 14. Their 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 they could sell it for on the open market. Their 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 they could sell it for on the open market. Indeed, you could assume that what they do is buy it on the open market and then immediately deliver it to you in the forward contract. Indeed, you could assume that what they do is buy it on the open market and then immediately deliver it to you in the forward contract. Their payoff is negative, however, if the market price of wheat is greater than $4.00/bushel. Their payoff is negative, however, if the market price of wheat is greater than $4.00/bushel. They could have sold the wheat for more than $4.00/bushel had they not agreed to sell it to you. They could have sold the wheat for more than $4.00/bushel had they not agreed to sell it to you. So their payoff function is the mirror image of your payoff function: So their payoff function is the mirror image of your payoff function: Forward Contracts

25. 25 Forward Contracts

26. 26 Forward Contracts Clearly the short position is just the mirror image of the long position, and, taken together the two positions cancel each other out: Clearly the short position is just the mirror image of the long position, and, taken together the two positions cancel each other out:

27. 27 Forward Contracts Long Position Net Position Short Position

28. 28 Futures Contracts A futures contract is similar to a forward contract in that it is an agreement between two parties to buy or sell an asset at a certain time for a certain price. Futures, however, are usually exchange traded and, to facilitate trading, are usually standardized contracts. This results in more institutional detail than is the case with forwards. A futures contract is similar to a forward contract in that it is an agreement between two parties to buy or sell an asset at a certain time for a certain price. Futures, however, are usually exchange traded and, to facilitate trading, are usually standardized contracts. This results in more institutional detail than is the case with forwards. The long and short party usually do not deal with each other directly or even know each other for that matter. The exchange acts as a clearinghouse. As far as the two sides are concerned they are entering into contracts with the exchange. In fact, the exchange guarantees performance of the contract regardless of whether the other party fails. The long and short party usually do not deal with each other directly or even know each other for that matter. The exchange acts as a clearinghouse. As far as the two sides are concerned they are entering into contracts with the exchange. In fact, the exchange guarantees performance of the contract regardless of whether the other party fails.

29. 29 Futures Contracts The largest futures exchanges are the Chicago Board of Trade (CBOT) and the Chicago Mercantile Exchange (CME). The largest futures exchanges are the Chicago Board of Trade (CBOT) and the Chicago Mercantile Exchange (CME). Futures are traded on a wide range of commodities and financial assets. Futures are traded on a wide range of commodities and financial assets. Usually an exact delivery date is not specified, but rather a delivery range is specified. The short position has the option to choose when delivery is made. This is done to accommodate physical delivery issues. Usually an exact delivery date is not specified, but rather a delivery range is specified. The short position has the option to choose when delivery is made. This is done to accommodate physical delivery issues. Harvest dates vary from year to year, transportation schedules change, etc. Harvest dates vary from year to year, transportation schedules change, etc.

30. 30 Futures Contracts The exchange will usually place restrictions and conditions on futures. These include: The exchange will usually place restrictions and conditions 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 a forward contract. Note however, that the basic payoffs are the same as for a forward contract.

31. Difference between forwards and futures 31

32. 32 Options Contracts Options on stocks were first traded in 1973. That was the year the famous Black-Scholes formula was published, along with Merton’s paper - a set of academic papers that literally started an industry. Options on stocks were first traded in 1973. That was the year the famous Black-Scholes formula was published, along with Merton’s paper - a set of academic papers that literally started an industry. Options exist on virtually anything. Today we are going to focus on general options terminology for stocks. Options exist on virtually anything. Today we are going to focus on general options terminology for stocks. There are two basic types of options: There are two basic types of options: A Call option is the right, but not the obligation, to buy the underlying asset by a certain date for a certain price. A Call option is the right, but not the obligation, to buy the underlying asset by a certain date for a certain price. A Put option is the right, but not the obligation, to sell the underlying asset by a certain date for a certain price. A Put option is the right, but not the obligation, to sell the underlying asset by a certain date for a certain price. Note that unlike a forward or futures contract, the holder of the options contract does not have to do anything - they have the option to do it or not. Note that unlike a forward or futures contract, the holder of the options contract does not have to do anything - they have the option to do it or not.

33. 33 Options Contracts The date when the option expires is known as the exercise date, the expiration date, or the maturity date. The date when the option expires is known as the exercise date, the expiration date, or the maturity date. The price at which the asset can be purchased or sold is known as the strike price. The price at which the asset can be purchased or sold is known as the strike price. If an option is said to be European, it means that the holder 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 is said to be an American style option, the holder can exercise on any date up to and including the exercise date. If an option is said to be European, it means that the holder 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 is said to be an American style option, the holder can exercise on any date up to and including the exercise date. An options contract is always costly to enter as the long party. The short party always is always paid to enter into the contract An options contract is always costly to enter as the long party. The short party always is always paid to enter into the contract Looking at the payoff diagrams you can see why… Looking at the payoff diagrams you can see why…

34. 34 Options Contracts Let’s say that you entered into a call option on IBM stock: Let’s say that you entered into a call option on IBM stock: Today 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 in December at a price of $80/share. Today 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 in December at a price of $80/share. If in December the market price of IBM were greater than $80, you would exercise your option, and purchase the IBM share for $80. If in December the market price of IBM were greater than $80, you would exercise your option, and purchase the IBM share for $80. 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, so you would not exercise your option. 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, so you would not exercise your option. Thus your payoff to the option is $0 if the IBM stock is less than $80 Thus your payoff to the option is $0 if the IBM stock is less than $80 It is (S T -K) if IBM stock is worth more than $80 It is (S T -K) if IBM stock is worth more than $80 Thus, your payoff diagram is: Thus, your payoff diagram is:

35. 35 Options Contracts T

36. 36 Options Contracts What if you had the short position? What if you had the short position? Well, after you enter into the contract, you have granted the option to the long-party. Well, after you enter into the contract, you have granted the 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 there best interest to do so – that is, when the strike price is lower than the market price of the stock. Of 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 than the market price of the stock. So if the stock price is less than the strike price (S T <K), then the long party will just buy the stock in the market, and so the option will expire, and you will receive $0 at maturity. So if the stock price is less than the strike price (S T <K), then the long party will just buy the stock in the market, and so the option will expire, and you will receive $0 at maturity. If the stock price is more than the strike price (S T >K), however, then the long party will exercise their option and you will have to sell them an asset that is worth S T for $K. If the stock price is more than the strike price (S T >K), however, then the long party will exercise their option and you will have to sell them an asset that is worth S T for $K. We can thus write your payoff as: We can thus write your payoff as: payoff = min(0,S T -K), which has a graph that looks like:

37. 37 Options Contracts

38. 38 Options Contracts 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 option position can NEVER have a positive payout – the best that can happen is that they get $0. Notice, however, that at maturity, the short option position can NEVER have a positive payout – the best that can happen is that they get $0. This is why the short option party always demands an up-front payment – it’s the only payment they are going to receive. This payment is called the option premium or price. This is why the short option party always demands an up-front payment – it’s the only payment they are going to receive. This payment is called the option premium or price. Once again, the two positions “net out” to zero: Once again, the two positions “net out” to zero:

39. 39 Options Contracts Long Call Short Call Net Position

40. 40 Options Contracts Recall that a put option grants the long party the right to sell the underlying at price K. Recall that a put option grants the long party the right to sell the underlying at price K. Returning to our IBM example, if K=80, the long party will only elect to exercise the option if the price of the stock in the market is less than $80, otherwise they would just sell it in the market. Returning to our IBM example, if K=80, the long party will only elect to exercise the option if the price of the stock in the market is less than $80, otherwise they would just sell it in the market. The payoff to the holder of the long put position, therefore is simply The payoff to the holder of the long put position, therefore is simply payoff = max(0, K-S T )

41. 41 Options Contracts

42. 42 Options Contracts The short position again has granted the option to the long position. The short has to buy the stock at price K, when the long party wants them to do so. Of course the long party will only do this when the stock price is less than the strike price. The short position again has granted the option to the long position. The short has to buy the stock at price K, when the long party wants them to do so. Of course the long party will only do this when the stock price is less 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, S T -K) And the payoff diagram looks like: And the payoff diagram looks like:

43. 43 Options Contracts

44. 44 Options Contracts Since the short put party can never receive a positive payout at maturity, they demand a payment up-front from the long party – that is, they demand that the long party pay a premium to induce them to enter into the contract. Since the short put party can never receive a positive payout at maturity, they demand a payment up-front from the long party – that is, they demand that the long party pay a premium to induce them to enter into the contract. Once again, the short and long positions net out to zero: when one party wins, the other loses. Once again, the short and long positions net out to zero: when one party wins, the other loses.

45. 45 Options Contracts Long Position Short Position Net Position

46. 46 Options Contracts The standard options contract is for 100 units of the underlying. Thus if the option is selling for $5, you would have to enter into a contract for 100 of the underlying stock, and thus the cost of entering would be $500. The standard options contract is for 100 units of the underlying. Thus if the option is selling for $5, you would have to enter into a contract for 100 of the underlying stock, and thus the cost of entering would be $500. For a European call, the payoff to the option is: For a European call, the payoff to the option is: Max(0,S T -K) Max(0,S T -K) For a European put it is For a European put it is Max(0,K-S T ) Max(0,K-S T ) The short positions are just the negative of these: The short positions are just the negative of these: Short call: -Max(0,S T -K) = Min(0,K-S T ) Short call: -Max(0,S T -K) = Min(0,K-S T ) Short put: -Max(0,K-S T ) = Min(0,S T -K) Short put: -Max(0,K-S T ) = Min(0,S T -K)

47. 47 Options Contracts Traders frequently refer to an option as being “in the money”, “out of the money” or “at the money”. Traders frequently refer to an option as being “in the money”, “out of the money” or “at the money”. An “in the money” option means one where the price of the underlying is such that if the option were exercised immediately, the option holder would receive a payout. An “in the money” option means one where the price of the underlying is such that if the option were exercised immediately, the option holder would receive a payout. For a call option this means that S t >K For a call option this means that S t >K For a put option this means that S t <K For a put option this means that S t <K An “at the money” option means one where the strike and exercise prices are the same. An “at the money” option means one where the strike and exercise prices are the same. An “out of the money” option means one where the price of the underlying is such that if the option were exercised immediately, the option holder would NOT receive a payout. An “out of the money” option means one where the price of the underlying is such that if the option were exercised immediately, the option holder would NOT receive a payout. For a call option this means that S t <K For a call option this means that S t <K For a put option this means that S t >K. For a put option this means that S t >K.

48. 48 Options Contracts T Out of the money In the money At the money

49. 49 Options Contracts One interesting notion is to look at the payoff from just owning the stock – its value is simply the value of the stock: One interesting notion is to look at the payoff from just owning the stock – its value is simply the value of the stock:

50. 50 Options Contracts

51. 51 Options Contracts What is interesting is if we compare the payout from a portfolio containing a short put and a long call with the payout from just owning the stock: What is interesting is if we compare the payout from a portfolio containing a short put and a long call with the payout from just owning the stock:

52. 52 Options Contracts

53. 53 Options Contracts Notice how the payoff to the options portfolio has the same shape and slope as the stock position – just offset by some amount? Notice how the payoff to the options portfolio has the same shape and slope as the stock position – just offset by some amount? This is hinting at one of the most important relationships in options theory – Put-Call parity. This is hinting at one of the most important relationships in options theory – Put-Call parity. It may be easier to see this if we examine the aggregate position of the options portfolio: It may be easier to see this if we examine the aggregate position of the options portfolio:

54. 54 Options Contracts

55. 55 Options Contracts So who trades options contracts? Generally there are three types of options traders: So who trades options contracts? Generally there are three types of options traders: Hedgers - these are firms that face a business risk. They wish to get rid of this uncertainty using a derivative. For example, an airline might use a derivatives contract to hedge the risk that jet fuel prices might change. Hedgers - these are firms that face a business risk. They wish to get rid of this uncertainty using a derivative. For example, an airline might use a derivatives contract to hedge the risk that jet fuel prices might change. Speculators - They want to take a bet (position) in the market and simply want to be in place to capture expected up or down movements. Speculators - They want to take a bet (position) in the market and simply want to be in place to capture expected up or down movements. Arbitrageurs - They are looking for imperfections in the capital market. Arbitrageurs - They are looking for imperfections in the capital market.