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Introduction

Introduction. A derivative is a financial instrument whose return is derived from the return on another instrument. Size of the derivatives market at year-end 2001: $3.8 trillion in market value All financial institutions can make some productive use of derivative assets Use of Derivatives:

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Introduction

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  1. Introduction • A derivative is a financial instrument whose return is derived from the return on another instrument. • Size of the derivatives market at year-end 2001: $3.8 trillion in market value • All financial institutions can make some productive use of derivative assets • Use of Derivatives: • Risk Management—Hedging and tuning risk to an acceptable level • Speculation and tactical asset allocation—Maximize thrust in a given asset class • Of course, arbitrage operations from temporally mispriced securities • Operational Advantages: Low transaction costs, very liquid, can be written (short-sold) easily

  2. Categories of Derivatives • Futures • Listed, OTC futures • Forward contracts • Options • Calls • Puts Derivatives • Swaps • Interest rate swap • Foreign currency swap

  3. Why Options Are a Good Idea • Increased risk • Instantaneous information • Portfolio risk management • Risk transfer • Financial leverage • Income generation

  4. Options Basics • A call option gives its owner the right to buy; it is not a promise to buy. A put option gives its owner the right to sell; it is not a promise to sell. • An American option gives its owner the right to exercise the option anytime prior to option expiration. A European option may only be exercised at expiration • Options giving the right to buy or sell shares of stock (stock options) are the best-known options. An option contract is for 100 shares of stock • The underlying asset of an index option is some market measure like the S&P 500 index. It is Cash-settled • Option characteristics • Expiration dates:The Saturday following the third Friday of certain designated months for most options • Striking price: The predetermined transaction price, in multiples of $2.50 or $5, depending on current stock price • Underlying Security: The security the option gives you the right to buy or sell. Both puts and calls are based on 100 shares of the underlying security

  5. Opening and Closing Transactions • The first trade someone makes in a particular option is an opening transaction • When the individual subsequently closes that position out with a second trade, this latter trade is a closing transaction • 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:1)Notify your broker; 2) Broker notifies the Options Clearing Corporation who selects a contra party to receive the exercise notice • The option premium is not a down payment on the purchase of the stock • The option holder, not the option writer, decides when and if to exercise • In general, you should not buy an option with the intent of exercising it • 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

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

  7. 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) • Bid PriceandAsk Price • Types of orders • Amarket order and limit order ( specifies a particular price (or better) beyond which no trade is desired. It requires a time limit, such as “for the day” or “good ‘til canceled (GTC)” • Margins

  8. MAY 2005 Underlying Symbol Last Sale Net Change Calls iShares Dow Jones US Telecommunications LastSale NetChg Bid Ask Vol OpenInterest Puts IYZ LastSale NetChg 23.15 Bid Ask 0.2000    Vol OpenInterest MAY 2005 20 IYZET $3.60 unch $3.20 $3.60 N.A. N.A. MAY 2005 20 IYZQT $0.35 unch $0.05 $0.10 N.A. 10 MAY 2005 21 IYZEU $0.85 unch $0.05 $0.15 N.A. 73 MAY 2005 21 IYZQU $0.30 unch $0.05 $0.10 N.A. 12 MAY 2005 22 IYZEV $0.05 unch $0.05 $0.05 13 2,200 MAY 2005 22 IYZQV $0.60 unch $0.80 $1.00 N.A. 35 MAY 2005 23 IYZEW $1.50 unch $0.90 $1.15 N.A. 52 MAY 2005 23 IYZQW $0.45 unch $0.15 $0.40 N.A. 3 MAY 2005 24 IYZEX $1.45 unch $0.40 $0.65 N.A. 15 MAY 2005 24 IYZQX N.A. N.A. $1.15 $1.40 N.A. N.A. MAY 2005 25 IYZEY $0.35 unch $0.15 $0.40 N.A. 4 MAY 2005 25 IYZQY $2.55 unch $2.10 $2.40 N.A. N.A. MAY 2005 26 IYZEZ $1.00 unch $0.00 $0.25 N.A. 2 MAY 2005 26 IYZQZ N.A. N.A. $3.10 $3.50 N.A. N.A.

  9. The Option Premium =Intrinsic Value + 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 =MAX(0,stock price –striking price) • For a put option, intrinsic value =MAX(0,striking price – stock price) • Intrinsic value cannot be < zero • Out, at and in-the -money • 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 • An option whose striking price is positive is in-the-money • 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) • AKA: speculative value • Difference between option premium and intrinsic value. • Speculative value=0 at maturity • Before, speculative value= the chance that the option will expire in-the-money; e.g., the intrinsic value is greater than zero!

  10. Intrinsic Value of Option • Value if option is exercised immediately= Intrinsic value: • Call option: MAX(0,S-X) • Put option: MAX(0,X-S) • In-the-money: • Call: S>X • Put: X>S • Out-of-the-money: • Call: S<X • Put: X<S • At-the-money: X=S • EXAMPLE 1: LONG,SHORT—CALL,PUT PAYOFFS AT MATURITY>

  11. Example 1 :Assume that you bought a call option 3 months ago at $10 with a strike at $100

  12. Example 1: Assume that you sold a call option 3 months ago at $10 with a strike at $100

  13. Expiration Date Payoffs to Long and Short Call Positions

  14. Example 1: Assume that you bought a put option 3 months ago at $10 with a strike at $100

  15. Example 1: Assume that you sold a put option 3 months ago at $10 with a strike at $100

  16. Expiration Date Payoffs to Long and Short Put Positions

  17. Put-Call-Spot Parity

  18. Put-Call-Spot Parity

  19. Put-Call-Spot Parity S + P - C = X(1 + Rf)-T • where: Rf = the annualized risk-free rate T = the time to maturity in years Let X(1 + Rf)-T = the proceed of a T-bill with a face value of X Then (long stock) + (long put) - (short call) = (long T-bill)

  20. Creating Synthetic SecuritiesUsing Put-Call Parity T-bill=S + P - C Put= X(1 + Rf)-T - S+ C Call = S + P - X(1 + Rf)-T Stock = X(1 + Rf)-T - P + C

  21. Portfolio Risk Management • Rational • How: • Narrowing the distribution • Diversification between classes • Beta positioning • “Skewing” the distribution to the left with Options • Covered call • Protective puts • How can the put-call parity be used in the risk management framework?

  22. Protecting Portfolio Value with Put Options • Protective puts • Hedges downside losses • Protective put=S+P=C+T-bill • Example 2: • Portfolio value = $100 million • 3-month put quote on Nasdaq100=52.96 (spot=4000, strike=4000) • 1 Nasdaq contract is based on a price of $400,000 (index price x 100=$400,000); the premium costs $5,296 for 1 contract(100 x 52.6) • you need 250 contracts ($ to hedge/$ of 1 contract = 100M/0.4M) • 3-month put premium 1.324 million (250 x 52.96 X100)

  23. Example 2 (continued): Expiration Date Value of a Protective Put Position

  24. Example 3: Protective Put RATIONAL: Investors may anticipate a decline in the value of an Investment but cannot conveniently sell. OPERATION: LONG PUT & LONG STOCK • INITIALLY, -So-Po • AT MATURITY: S(T)+MAX(X-S(T),0) • PROFIT (AT MATURITY)= S(T)+MAX(X-S(T),0)-So-Po EXAMPLE: purchased Microsoft for $28.51 and a Microsoft APR 25 put for $1.10 BREAKEVEN: IF S(T)<X, S(T)+X-S(T)-So-Po=0 NO SOLUTIONS FOR S(T) IF S(T)>X, S(T)-So-Po=0S(T)=So+Po=28.51+1.1=29.61 IN SUM: -The maximum loss is $4.61 -The maximum loss occurs at all stock prices of $25 or below -The put breaks even somewhere between $25 and $30 (it is exactly $29.61) -The maximum gain is unlimited

  25. Logic Behind the Protective Put • 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 • A protective put is an example of a synthetic call

  26. Altering Portfolio Payoffs with Call Options • Covered calls • Call writer owns the stock: S-C=T-bill - P • Benefits • If you wish, the cash received from the sell of the calls shifts the downside potential up; this is a dangerous strategy that may be used to profit in a “neutral-bearish” and low volatility market • Danger • Prices could fall very very badly.

  27. Example 4 A fund manager writes covered calls against the $100 million fund and receives the premium of $2.813 million, The calls have been chosen so that the strike is 100 million (ATM) if your portfolio follows the NASDAQ100, which is quoted at 4000, a 3-month “at-the money” option (strike is 4000) is priced at 112.52. 1 contract is 100 times the index, so a call with a strike at 4000 correspond to $400,000 and is priced at $11,252. You need to cover $100,000,000; thus, you need 250 contracts (100m/0.4), which cost in total $2.813 M (11,252 x 250). .

  28. Example 4 (continued): Altering Portfolio Payoffs with Call Options

  29. Example 5: Questions • What are the advantages of a covered call strategy? • Under what circumstance(s) would you use a covered call strategy Vs. a protective put strategy? • Your portfolio is not traded in the option market; only index options are traded. How would set the number of puts to buy or calls to sell in practice?

  30. Example 6: Covered Calls • Rational: Useful for investors anticipating a drop in the market but unwilling to sell the shares now • Operation: Long stock and short call Initially: -So+Co At maturity: S(T)-Max(S(T)-X,0) Profit at maturity: -So+Co+S(T)-Max(S(T)-X,0) • Example: Write a JAN 30 covered call on Microsoft @ $1.20; buy stock @ 28.51 • Break-even: -So+Co+S(T)-Max(S(T)-X,0)=0 If S<X, -So+Co+S(T)=0S(T)=So-C0=28.51-1.20=27.31 If S>X, -So+Co+S(T)-S(T)+X=0No solution • In sum: The call premium cushions the loss. This is a synthetic short put.

  31. LONG SHORT Speculating with options STRADDLE (Same X,M) C+P -C-P STRANGLE (≠ X, same M) C(ITM)+P(OTM) -C(ITM)-P(OTM) STRAP (Same X,M) 2C+P -C-2P SPREAD (≠ X, same M) C(ITM)-C(ATM) P(ITM)-P(ATM) C-BUTTERFLY (≠ X, same M) C(OTM)-2C(ATM)+C(ITM) -C(OTM)+2C(ATM)-C(ITM) • Playing with expected volatility and expected changes in market conditions.

  32. Sample of quoted options with 6 months maturity

  33. Example 7: Terminal payoff for Long straddle (C+P) and short straddle (-C-P): same maturity and strike price (call 2 and Put 2)

  34. Example 8: Buying a Straddle • A long call is bullish; A long put is bearish • Why buy a long straddle? • Whenever a situation exists when it is likely that a stock will move sharply one way or the other • Suppose a speculator • Buys a JAN 30 call on MSFT @ $1.20 • Buys a JAN 30 put on MSFT @ $2.75 • Equation: Max(S(T)-X,0)-Co+Max(X-S(T),0)-Po • Breakeven:Max(S(T)-X,0)-Co+Max(X-S(T),0)-Po=0 2 cases: (1) S<X, then -Co+X-S(T)-Po=0 S(T)=-Co+X-Po=-1.2+30-2.75=26.05 (2) S>X, then S(T)-X-Co-Po=0 S(T)=X+Co+Po=30+1.2+2.75=33.95 • The worst outcome for the straddle buyer is when both options expire worthless. It occurs when the stock price is at-the-money. So the straddle buyer will lose money if stock closes near the striking price

  35. Example 9: Strangles • A strangle is similar to a straddle, except the puts and calls have different striking prices.The speculator long a strangle expects a sharp price movement either up or down in the underlying security • With a long strangle, the most popular version involves buying a put with a lower striking price than the call • Suppose a speculator: • Buys a MSFT JAN 25 put @ $0.70 • Buys a MSFT JAN 30 call @ $1.20

  36. Example 10: Condors Long Condor • A condor is a less risky version of the strangle, with four different striking prices • The condor buyer hopes that stock prices remain in the range between the middle two striking prices • Buyer: • Buys MSFT 25 calls @ $4.20 • Writes MSFT 27.50 calls @ $2.40 • Writes MSFT 30 puts @ $2.75 • Buys MSFT 32.50 puts @ $4.60 • Seller: • writes MSFT 25 calls @ $4.20 • buys MSFT 27.50 calls @ $2.40 • buys MSFT 30 puts @ $2.75 • writes MSFT 32.50 puts @ $4.60 Short Condor

  37. Sample of quoted options with 6 months maturity

  38. Example 11: Long Strap: 2 C + P (same maturity and strike)

  39. Sample of quoted options with 6 months maturity

  40. Example 12: “Bull spread”: buy call no 1 (in-the money) and sell call no 3 (out-the money)

  41. Comparing the Bull Money Spread and Long Call Positions

  42. Sample of quoted options with 6 months maturity

  43. Example 13: “Bear Spread”:buy put no 3 (in-the money) and sell put no l (out-the money).

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