Fin 603 Week 11

1. Fin 603 Week 11 Options

2. What is a Derivative Security? • A security whose value is “derived” from something else, using a security, a collection of securities, or anything that has a price or probability attached to it • Derivatives are primarily used to “shape risk” • The three main kinds of derivative securities: • Futures contracts • Swaps • Options Professor Ross Miller • Fall 2005

3. A Few More Words on Futures • Stock index futures • Pricing works the same as gold futures—price goes up by the full carryin cost (determined by the risk-free rate of return) • Futures, in general • Typical energy and agricultural futures do not rise in line with the full carrying cost • Seasonal and temporary factors make their prices fall more in line with the expectations of the market Professor Ross Miller • Fall 2005

4. A Full Carrying Charge Market • A full carrying charge market occurs when the futures price reflects the cost of storing and financing the commodity until the delivery month • The futures price is equal to the current spot price plus the carrying charge: Professor Ross Miller • Fall 2005

5. Contango and Backwardation • Basis is the difference between the future price of a commodity and the current cash price • Normally, the futures price exceeds the cash price (contango market) • The futures price may be less than the cash price (backwardation or inverted market) Professor Ross Miller • Fall 2005

6. Normal Backwardation(John Maynard Keynes) • Locking in a future price that is acceptable eliminates price risk for the hedger • The speculator must be rewarded for taking the risk that the hedger was unwilling to bear • Thus, at delivery, the cash price will likely be somewhat higher than the price predicated by the futures market Professor Ross Miller • Fall 2005

7. Stock Index Futures in March 2005 Fifteen-minute delayed quotes from CME Professor Ross Miller • Fall 2005

8. Heating Oil Futures in March 2005 Professor Ross Miller • Fall 2005

9. A Few More Words on Swaps • Interest rates swaps are just a bundle of forward rate agreements (FRAs) • FRAs are priced off the yield curve • Swap prices (in percentage yields) are approximately the average of the forward rates • The swap price represents the fixed rate that is an even trade-off for the bundle of FRAs • Many other types of instruments called “swaps” exist, but most of them are just complicated forward contracts Professor Ross Miller • Fall 2005

10. Some Option Basics • Options provide the opportunity to buy (call option) or sell (put option) something at a given exercise price on or before a given expiration date • Options that restrict exercise to the expiration date are known as European options. Such options are rare in the U.S., and so the standard kind of option is known as an American option Professor Ross Miller • Fall 2005

11. The Benefits of Holding Call Options • Insurance: Protection against major price declines • Leverage: Increases returns relative to holding stock in an up market • The Catch: You are paying for both the insurance and the implicit “rental” of the stock Professor Ross Miller • Fall 2005

12. Options are Everywhere • We have already seen the prepayment option in mortgages • The ability of a company to default on its debt can be viewed as an option • The ability of equity holders to walk away from their company and cede control to debt holders is an option • Even limit orders and market maker’s quote provide options Professor Ross Miller • Fall 2005

13. Where Traded Options Come From • Unlike stocks and bonds (and like futures and swaps), there is no fixed number of put or call options • The number in existence changes every day • This number is called the open interest • Similarly, futures contracts have open interest • Stocks, on the other hand, have shares outstanding, which the issuer can only change by buying or floating shares Professor Ross Miller • Fall 2005

14. Opening and Closing Transactions • The first trade someone makes in a particular option is an opening transaction for that person • When the individual subsequently closes that position out with a second trade, this latter trade is a closing transaction Professor Ross Miller • Fall 2005

15. Opening and Closing Transactions (cont’d) • When someone buys an option as an opening transaction, the owner of an option will ultimately do one of three things with it: • Sell it to someone else • Let it expire • Exercise it Professor Ross Miller • Fall 2005

16. Opening and Closing Transactions (cont’d) • When someone sells an option as an opening transaction, this is called writing the option • No matter what the owner of an option does, the writer of the option keeps the option premium that he or she received when it was sold Professor Ross Miller • Fall 2005

17. Role of the Options Clearing Corporation (OCC) • The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the options market • The OCC positions itself between every buyer and seller and acts as a guarantor of all option trades • The OCC sets minimum capital requirements and provides for the efficient transfer of funds among members as gains or losses occur Professor Ross Miller • Fall 2005

18. Exchanges • Major options exchanges in the U.S.: • Chicago Board Options Exchange (CBOE) • American Stock Exchange (AMEX) • Philadelphia Stock Exchange (Philly) • Pacific Stock Exchange (PSE) • International Securities Exchange (ISE) • These exchanges are equal owners of the OCC • Options are traded on exchanges in most countries with organized securities markets Professor Ross Miller • Fall 2005

19. Over-the-Counter (OTC)Options • With an over-the-counter option: • Institutions enter into “private” option arrangements with brokerage firms or other dealers • The striking price, life of the option, and premium are negotiated between the parties involved • Over-the-counter or OTC options are subject to counterparty risk and are generally not fungible • OTC options tend to be cost significantly more than their “theoretical value,” while traded options trade close to that value Professor Ross Miller • Fall 2005

20. Some Not-So-Exotic “Exotic” Options • Asian or average price option • Payoff based on the average price of the underlying over the life (or some part of the life) of the option • Barrier option • Option that is either activated (an “in” option) or cancelled (an “out” option) when the underlying prespecified price level is reached • Binary option • Option that pays out zero or a fixed amount Professor Ross Miller • Fall 2005

21. ClickOptions (Blurring the Boundary Between Options and Gambling) Professor Ross Miller • Fall 2005

22. Intrinsic Value and Time Value • Intrinsic value is the amount that an option is immediately worth given the relation between the option striking price and the current stock price • For a call option, intrinsic value = stock price – striking price • For a put option, intrinsic value = striking price – stock price • Intrinsic value cannot be < zero Professor Ross Miller • Fall 2005

23. Intrinsic Value and Time Value (cont’d) • An option with no intrinsic value is out-of-the-money • An option whose striking price is exactly equal to the price of the underlying security is at-the-money • Options that are “almost” at-the-money are near-the-money Professor Ross Miller • Fall 2005

24. Intrinsic Value and Time Value (cont’d) • Time value is equal to the premium minus the intrinsic value • As an option moves closer to expiration, its time value decreases (time value decay), making it awasting asset Professor Ross Miller • Fall 2005

25. Profit and Loss Diagrams • Vertical axis reflects profits or losses on the expiration day resulting from a particular strategy • Horizontal axis reflects the stock price on the expiration day • Bends in the diagram occurs at the striking prices • By convention, diagrams ignore the effect of transactions costs, including commissions Professor Ross Miller • Fall 2005

26. Going Long a Call Option • Example: buy a Microsoft October 25 call for $3.70 • Maximum loss is $3.70 • Profit potential is unlimited • Breakeven at expiration is a stock price of $28.70 Professor Ross Miller • Fall 2005

27. Going Long a Call Option (cont’d) Breakeven = $28.70 0 10 15 20 25 30 Maximum loss = $3.70 Professor Ross Miller • Fall 2005

28. A Problem with the Standard Payoff Diagram • You pay for the option now • You get the option payoff (if any) in the future • In looking at the payoff diagram, you should use the future value of the option • This future value is difficult to compute, in particular, you cannot use the risk-free rate to discount the option • See my first Financial Engineering News“Capital Notions” column for details Professor Ross Miller • Fall 2005

29. Writing or Going Short a Call Option • Ignoring commissions, the options market is a zero sum game • Aggregate gains and losses will always net to zero • The most an option writer can make is the option premium • Writing a call without owning the underlying shares is called writing a naked (uncovered) call Professor Ross Miller • Fall 2005

30. A Key Observation • If an option expires out of the money (below the exercise price in the case of a call option), it does not matter how far out of the money it expires • If one compares options on two otherwise identical stock with different volatility, the option on the more volatile stock is worth more • The more volatility stock has a greater expected upside • It also has a greater expected downside, but that does not matter Professor Ross Miller • Fall 2005

31. Writing a Call Option (cont’d) Breakeven = $28.70 Maximum Profit = $3.70 0 10 15 20 25 30 Professor Ross Miller • Fall 2005

32. Going Long a Put Option • Example: buy a Microsoft April 25 put for $1.10 • Maximum loss is $1.10 • Maximum profit is $23.90 • Breakeven at expiration is a stock price of $23.90 Professor Ross Miller • Fall 2005

33. Buying a Put Option (cont’d) $23.90 Breakeven = $23.90 0 10 15 20 25 30 $1.10 Professor Ross Miller • Fall 2005

34. Some Nov 2005 Google Call OptionsFrom 11/15/2005 with GOOG at 392.00 StrikeSymbolLastChgBidAskVolOpen Int 370.00 GGDKN.X 22.20 – 5.10 22.10 22.40 561 5,923 380.00 GOPKP.X 12.90 – 4.70 12.70 13.00 2,369 10,638 390.00 GOPKR.X 5.40 – 3.70 5.40 5.60 4,075 17,460 400.00 GOPKT.X 1.70 – 2.10 1.60 1.75 5,959 19,564 Professor Ross Miller • Fall 2005

35. Some Nov 2005 Google Put OptionsFrom 11/15/2005 with GOOG at 392.00 StrikeSymbolLastChgBidAskVolOpen Int 370.00 GGDWN.X 0.20 – 0.10 0.20 0.30 315 9,150 380.00 GOPWP.X 0.80 + 0.15 0.80 0.90 1,482 17,939 390.00 GOPWR.X 3.50 + 1.35 3.40 3.50 4,235 17,409 400.00 GOPWT.X 9.60 + 3.10 9.60 9.90 1,276 5,382 Professor Ross Miller • Fall 2005

36. Writing (or Going Short) a Put Option • The put option writer has the obligation to buy if the put is exercised by the holder Professor Ross Miller • Fall 2005

37. Writing a Put Option (cont’d) Breakeven = $23.90 $1.10 0 10 15 20 25 30 $23.90 Professor Ross Miller • Fall 2005

38. A Note on Margin Requirements • A margin requirement is analogous to posting collateral and can be satisfied by a deposit of cash or other securities into your brokerage account • The margin system is to reduce the likelihood that option writers will be unable to fulfill their obligations Professor Ross Miller • Fall 2005

39. Protective Puts • A protective put is a descriptive term given to a long stock position combined with a long put position • Investors who use protective puts may anticipate a decline in the value of an investment but cannot or may not want to sell Professor Ross Miller • Fall 2005

40. Microsoft Example Assume you purchased Microsoft for $28.51 Profit or loss ($) 0 Stock price at option expiration 28.51 28.51 Professor Ross Miller • Fall 2005

41. Microsoft Example (cont’d) Assume you purchased a Microsoft APR 25 put for $1.10 23.90 23.90 25 0 Stock price at option expiration 1.10 Professor Ross Miller • Fall 2005

42. “Add” the Two Diagrams Together Protective put 25 0 Stock price at option expiration 29.61 4.61 Professor Ross Miller • Fall 2005

43. The Logic Behind Protective Puts • A protective put is like an insurance policy • You can choose how much protection you want • The put premium is what you pay to make large losses impossible • The striking price puts a lower limit on your maximum possible loss, like the deductible in car insurance • The more protection you want, the higher the premium you are going to pay Professor Ross Miller • Fall 2005

44. The “Greenspan Put” • It was generally believed that Alan Greenspan would act (by easing monetary policy) • This protection that he was thought to provide to the stock market became known as the Greenspan put Professor Ross Miller • Fall 2005

45. Option Combinations • Options are usually used in combinations to either place specific types of “bets” on a security (or related securities) or to create a specific hedge • Straddles (the simultaneous purchase of a matching put and call) is a common way to betting on increasing volatility • Options are so flexibility that any payoff diagram that you can draw can be approximated with a combination of options Professor Ross Miller • Fall 2005

46. Synthetic Options and Synthetic Equity • The term synthetic option describes a collection of financial instruments that are equivalent to an option position • A protective put is an example of a synthetic call long stock + long put  long call • More importantly, this also means (in an approximate sense) that one can create synthetic equity as follows: long stock  long call - long put Professor Ross Miller • Fall 2005

47. One Technicality • The synthetic stock in the previous slide is not stock “now” • Instead, it is a forward contract on stock that is delivered at the expiration date of the two options • The price of this forward contract can be computed using the standard FV formula with the risk-free rate as the full carrying cost Professor Ross Miller • Fall 2005

48. Put-Call Parity • Basic Idea: The price of the synthetic stock should (by an arbitrage argument) be the same as the difference in prices between the call the and the put • Two important assumptions • All options are European (no early exercise) • The stock pays no dividends (or them are known and can be PV’ed away) Professor Ross Miller • Fall 2005

49. The Put-Call Parity Formula (rearranged slightly from the BKM versions) Professor Ross Miller • Fall 2005

50. Putting a Value on Options Prior to Expiration • Two related approaches • Look at all the future possibilities and create an “average” payoff for the option that is the basis for its value • Decompose the option into pieces with known values and find the value of the options by adding up the values of the pieces • Key conceptual issues • What is the distribution of future values? • How do we discount them? Professor Ross Miller • Fall 2005