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Chapter 7: Advanced Option Strategies

Chance/Brooks. An Introduction to Derivatives and Risk Management, 7th ed.. Ch. 7: 2. Important Concepts. Profit equations and graphs for option spread strategies, including money spreads, collars, calendar spreads and ratio spreadsProfit equations and graphs for option combination strategies incl

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Chapter 7: Advanced Option Strategies

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    1. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 1 Chapter 7: Advanced Option Strategies I think reporters make a mistake when they say that speculation is inherently bad. Anyone who is involved with money has to take risks … To write about risk as if it's foreign to business is missing the essential nature of what businesses do. Saul Hansell The New York Times, Fall, 1995, p. 63

    2. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 2 Important Concepts Profit equations and graphs for option spread strategies, including money spreads, collars, calendar spreads and ratio spreads Profit equations and graphs for option combination strategies including straddles and box spreads

    3. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 3 Option Positions Naked positions Purchase or sale of a single security such as a stock or a call or a put. Hedged Positions Position in the stock together with options that provide partial or full protection from unfavorable outcomes. Spread positions Long one option and short another option on the same underlying security. Combinations Portfolio containing either long or short position in call and put options on the same underlying security.

    4. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 4 Option Spreads: Basic Concepts Spread Taking position in two or more options of the same type (i.e., two or more calls or two or more puts). vertical, strike, money spread horizontal, time, calendar spread diagonal spread Spread notation June 120/125 June/July 120 June 120/July 125 Long or short long, buying, debit spread short, selling, credit spread

    5. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 5 Option Spreads: Basic Concepts Vertical, Strike, Money Spreads The simultaneous purchase and sale of options identical in all respects except for strike price. Horizontal, Time, Calendar Spreads The simultaneous purchase and sale of options identical in all respects except time to expiration. Diagonal Spreads The simultaneous purchase and sale of options that differ in both strike price and time to expiration

    6. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 6 Vertical Spreads

    7. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 7 Horizontal Spreads

    8. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 8 Diagonal Spreads

    9. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 9 Option Spreads: Basic Concepts (continued) Why Investors Use Option Spreads Risk reduction To lower the cost of a long position Types of spreads bull spread: benefiting from stock price increase bear spread: benefiting from stock price decrease horizontal, time, calendar spread is based on volatility

    10. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 10 Option Spreads: Basic Concepts (continued) Notation For vertical, strike, money spreads X1 < X2 < X3 C1, C2, C3 N1, N2, N3 For horizontal, time, calendar spreads T1 < T2 C1, C2 N1, N2 See Table 7.1, p. 220 for DCRB option data

    11. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 11 Vertical, Strike, Money Spreads Bull Spreads Buy call with lower strike (X1) and sell call with higher strike (X2). See Figure 7.1, p. 222 for DCRB June 125/130, C1 = $13.50, C2 = $11.35. Maximum profit = X2 - X1 - C1 + C2, Minimum = - C1 + C2 Breakeven: ST* = X1 + C1 - C2 = $125 + $13.50 - $11.35 = $127.15

    12. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 12 Profit from Call Bull Spread

    13. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 13 Vertical, Strike, Money Spreads (continued) Bull Spreads (continued) For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 7.2, p. 223. Note how time value decay affects profit for given holding period. Early exercise not a problem.

    14. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 14 Call Bull Spread: Choice of Holding Period

    15. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 15 Vertical, Strike, Money Spreads (continued) Bear Spreads Buy put with higher strike (X2) and sell put with lower strike (X1) See Figure 7.3, p. 225 for DCRB June 130/125, P1 = $11.50, P2 = $14.25. Maximum profit = X2 - X1 + P1 - P2. Minimum = P1 - P2. Breakeven: ST* = X2 + P1 - P2 = $130 + $11.50 - $14.25 = $127.25

    16. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 16 Vertical, Strike, Money Spreads (continued) Bear Spreads (continued) For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 7.4, p. 226. Note how time value decay affects profit for given holding period. Note early exercise problem. A Note About Put Money Spreads Can construct call bear and put bull spreads.

    17. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 17 Profit from Put Bull Spread

    18. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 18 Call Bear Spread

    19. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 19 Vertical, Strike, Money Spreads (continued) Collars Buy stock, buy put with strike (X1) lower than current stock price and sell call with strike (X2) higher than current stock price. The investor is willing to sell the stock at a maximum price of X2, in exchange for which the investor receives the assurance that the stock will be sold for no worse than X1. A common type of collar is what is often referred to as a zero-cost collar. The call strike is set such that the call premium offsets the put premium so that there is no initial outlay for the options.

    20. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 20 Collar Payoff

    21. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 21 Vertical, Strike, Money Spreads (continued) Collars (continued) See Figure 7.5, p. 228 for DCRB July 120/136.165, P1 = $13.65, C2 = $13.65. That is, a call strike of 136.165 generates the same premium as a put with strike of 120. This result can be obtained only by using an option pricing model and plugging in exercise prices until you find the one that makes the call premium the same as the put premium. This will nearly always require the use of OTC options. Maximum profit = X2 - S0. Minimum = X1 - S0. Breakeven: ST* = S0 = $125.94

    22. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 22 Vertical, Strike, Money Spreads (continued) Collars (continued) The collar is a lot like a bull spread (compare Figure 7.5 to Figure 7.1). The collar payoff exceeds the bull spread payoff by the difference between X1 and the interest on X1. Thus, the collar is equivalent to a bull spread plus a risk-free bond paying X1 at expiration. For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 7.6, p. 229.

    23. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 23 Vertical, Strike, Money Spreads (continued) Butterfly Spreads Positions in options with three different strike prices. Buy two calls, one with a relatively low strike price and one with a relatively high strike price and sell two calls with the same strike price in the middle. For example, buy one July 120 call and one July 130 call and sell two July 125 calls. See Figure 7.7, p. 233 for DCRB July 120/125/130, C1 = $16.00, C2 = $13.50, C3 = $11.35. The sale of a butterfly spread involves selling two calls, one with a relatively low strike price and one with a relatively high strike price and buying two calls with the same strike price in the middle.

    24. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 24 Profit from Butterfly Spread

    25. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 25 Profit from Sale of Butterfly Spread

    26. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 26 Vertical, Strike, Money Spreads (continued) Butterfly Spreads (continued) Maximum profit = X2 - X1 - C1 + 2C2 - C3, minimum = -C1 + 2C2 - C3 Breakeven: ST* = X1 + C1 - 2C2 + C3 and ST* = 2X2 - X1 - C1 + 2C2 - C3 For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 7.8, p. 234. Note how time value decay affects profit for given holding period. Note early exercise problem.

    27. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 27 Horizontal, Time, Calendar Spreads Buy call with longer time to expiration, sell call with shorter time to expiration. Note how this strategy cannot be held to expiration because there are two different expirations. Profitability depends on volatility and time value decay. Use Black-Scholes-Merton model to value options at end of holding period if prior to expiration. See Figure 7.9, p. 235. Note time value decay. See Table 7.2, p. 236 and Figure 7.10, p. 237. Early exercise can be problem. Can be constructed with puts as well.

    28. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 28 Horizontal, Time, Calendar Spread Using Calls

    29. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 29 Horizontal, Time, Calendar Spread Using Puts

    30. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 30 Ratio Spreads Long one option, short another based on deltas of two options. Designed to be delta-neutral. Portfolio value V = N1C1 - N2C2 Set N1D1 - N2D2 to zero and solve for N1/N2 = D2/D1, which is ratio of their deltas (recall that D = N(d1) from Black-Scholes-Merton model). Buy June 120s, sell June 125s. Delta of 120 is 0.630; delta of 125 is 0.569. Ratio is (0.569/0.630) = 0.903. For example, buy 903 June 120s, sell 1,000 June 125s Changes in call prices (for small change in stock price) offset each other, i. e, the gain in one call offsets the loss on the other. Hedging mispriced option, i.e., buy under- (or correctly) valued and sell over- (or correctly) valued calls. The ratio should be continuously adjusted to remain riskless.

    31. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 31 Straddles Buying call and put on the same underlying security, with same strike price and time to expiration. Either call or put will be exercised (unless ST = X). See Figure 7.11, p. 240 for DCRB June 125, C = $13.50, P = $11.50. Breakeven: ST* = X - C - P and ST* = X + C + P Maximum profit: ?, minimum = - C - P See Figure 7.12, p. 242 for different holding periods. Note time value decay.

    32. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 32 Profit from Straddle

    33. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 33 Variations of Straddles Strangle Buying a call with a higher strike price and a put with a lower strike price (both with same expiration date). Strap Buying two calls and one put same strike price and expiration date. Strip Buying two puts and one call with same strike price and expiration date.

    34. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 34 Profit from Strangle

    35. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 35 Profit from Strap

    36. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 36 Strip versus Strap

    37. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 37 Straddles (continued) Applications of Straddles Based on perception of volatility greater than priced by market. A Short Straddle Unlimited loss potential Based on perception of volatility less than priced by market.

    38. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 38 Box Spreads Construction: Buy call with strike X1, sell call with strike X2 Buy put with strike X2, sell put with strike X1 Risk-free payoff if options are European Combination of a bull call money spread and a bear put money spread.

    39. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 39 Box Spreads (continued)

    40. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 40 Box Spreads (continued)

    41. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 41 Box Spreads (continued) Evaluate by determining net present value (NPV) NPV = (X2 - X1)(1 + r)-T - C1 + C2 - P2 + P1 This determines whether present value of risk-free payoff exceeds initial value of transaction. If NPV > 0, do it. If NPV < 0, do the reverse. See Figure 7.13, p. 245. Box spread is also difference between two put-call parities.

    42. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 42

    43. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 43 Box Spreads (continued)

    44. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 44 Box Spreads (continued) Evaluate June 125/130 box spread Buy 125 call at $13.50, sell 130 call at $11.35 Buy 130 put at $14.25, sell 125 put at $11.50 Initial outlay = $4.90; $490 for 100 each NPV = 100[(130 - 125)(1.0456)-0.0959 - 4.90] = $7.87 NPV > 0 so do it Early exercise a problem only on short box spread Transaction costs high

    45. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 45 Advanced Option Strategies

    46. Chance/Brooks An Introduction to Derivatives and Risk Management, 7th ed. Ch. 7: 46

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