Lecture 1.2: Advanced Option Strategies

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1 Option Strategies Covered Lecture 1.2: Advanced Option Strategies Profit equations and graphs for option spread strategies, including Bull spreads Bear spreads Collars Butterfly spreads : Financial Instrument and Innovation Nattawut Jenwittayaroje, Ph.D., CFA NIDA Business School Profit equations and graphs for option combination strategies including Straddles 1 2 Option Spreads: Basic Concepts (continued) Bull Spreads Notation For spreads X 1 < X 2 < X 3 Bull Spreads A bull spread consists of the purchase of the call option with the lower exercise price and the sale of the call option with the higher exercise price. C 1, C 2, C 3 That is, buy call with strike X 1, sell call with strike X 2. Let N 1 = 1, N 2 = -1 N 1, N 2, N 3 Profit equation: Π = Max(0,S T - X 1 ) - C 1 - Max(0,S T - X 2 ) + C 2 See Table 7.1 below for DCRB option data Π = -C 1 + C 2 if S T X 1 < X 2 Π = S T - X 1 - C 1 + C 2 if X 1 < S T X 2 Π = X 2 - X 1 - C 1 + C 2 if X 1 < X 2 < S T Maximum profit = X 2 - X 1 - C 1 + C 2, Minimum = - C 1 + C 2 Breakeven: S T* = X 1 + C 1 - C 2 3 4

Bull Spreads Bull Spreads Example See Figure 7.1 for DCRB June 125/130, C 1 = $13.50, C 2 = $11.35. That is, buy call with strike 125, sell call with strike 130.

2 Bull Spreads Bull Spreads Example See Figure 7.1 for DCRB June 125/130, C 1 = $13.50, C 2 = $ That is, buy call with strike 125, sell call with strike 130. Let N 1 = 1, N 2 = -1 Profit equation: Π = Max(0,S T - 125) Max(0,S T - 130) Π = = if S T 125 < 130 Π = S T = S T if 125 < S T 130 Π = = 2.85 if 125 < 130 < S T Maximum profit = = 2.85 Minimum = = Breakeven: S T* = = A call bull spread has a limited gain, which occurs in a bull market, and a limited loss, which occurs in a bear market. Long call at X=125 Short call at X= Bull Spreads (continued) Bear Spreads Bull Spreads (continued) A call bull spread has a limited gain, which occurs in a bull market, and a limited loss, which occurs in a bear market. In comparison to simply buying the 125 call, the spread trader reduces the maximum loss by the premium on the short 130 call and lowers the breakeven, but gives up the chance for large gains if the stock moves up substantially. Bear Spreads A bear spread is the mirror of a bull spread. We long the high-exercise-price put and short the low-exercise-price put. That is, buy put with strike X 2, sell put with strike X 1. Let N 1 = -1, N 2 = 1 Profit equation: Π = -Max(0,X 1 - S T ) + P 1 + Max(0,X 2 - S T ) - P 2 Π = X 2 - X 1 + P 1 - P 2 if S T X 1 < X 2 Π = P 1 + X 2 - S T - P 2 if X 1 < S T < X 2 Π = P 1 - P 2 if X 1 < X 2 S T Maximum profit = X 2 - X 1 + P 1 - P 2. Minimum = P 1 - P 2. Breakeven: S T* = X 2 + P 1 - P

Bear Spreads (continued) Bear Spreads Example See Figure 7.3, p. 225 for DCRB June 130/125, P 1 = $11.50, P 2 = $14.25. That is, buy put with strike 130, sell put with strike 125.

3 Bear Spreads (continued) Bear Spreads Example See Figure 7.3, p. 225 for DCRB June 130/125, P 1 = $11.50, P 2 = $ That is, buy put with strike 130, sell put with strike 125. Let N 1 = -1, N 2 = 1 Profit equation: Π = -Max(0,125 - S T ) Max(0,130 - S T ) Π = if S T 125 < 130 Π = S T if 125 < S T < 130 Π = if 125 < 130 S T Maximum profit = Minimum = Breakeven: S T* = Long put at X=130 A put bear spread has a limited gain, which occurs in a bear market, and a limited loss, which occurs in a bull market. Short put at X=125 (Return to text slide) 9 10 Bear Spreads (continued) Collars Bear Spreads (continued) A put bear spread has a limited gain, which occurs in a bear market, and a limited loss, which occurs in a bull market. In comparison to simply buying the 130 put, the spread trader reduces the maximum loss by the premium on the short 125 put and moves up the breakeven, but gives up the chance for large gains if the stock goes down substantially. Collars A collar is a strategy in which the holder of a position in a stock buys a put with an exercise price lower than the current stock price and sells a call with an exercise price higher than the current stock price. The call premium is intended to reduce the cost of the put premium. Buy stock, buy put with strike X 1, sell call with strike X 2. N S = 1, N P = 1, N C = -1. Profit equation: Π = S T - S 0 + Max(0,X 1 - S T ) - P 1 - Max(0,S T - X 2 ) + C 2 Π = X 1 - S 0 - P 1 + C 2 if S T X 1 < X 2 Π = S T - S 0 - P 1 + C 2 if X 1 < S T < X 2 Π = X 2 - S 0 - P 1 + C 2 if X 1 < X 2 S T Maximum profit = X 2 - S 0. Minimum = X 1 - S 0. Breakeven: S T* = S This term is usually set such that it is practically zero. 12

4 Collars (continued) 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. See Figure 7.5 for DCRB July 120/ , P 1 = $13.65, C 2 = $ That is, a call strike of 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 Profit equation: Π = if S T 120 < Π = S T if 120 < S T < Π = if 120 < S T Maximum profit = Minimum = Breakeven: S T* = Long put at X=120 Short call at X= Butterfly Spreads (continued) Butterfly Spreads (continued) Butterfly Spreads Butterfly spread is a combination of a bull spread and a bear spread. Specifically, buy call (put) with strike X 1, buy call (put) with strike X 3, sell two calls (puts) with strike X 2. X 2 is usually the halfway between X 1 and X 3. Let N 1 = 1, N 2 = -2, N 3 = 1. Profit equation: Π = Max(0,S T - X 1 ) - C 1-2Max(0,S T - X 2 ) + 2C 2 + Max(0,S T - X 3 ) - C 3 Butterfly Spread Using Calls Profit Butterfly Spread Using Puts Profit Π = -C 1 + 2C 2 - C 3 if S T X 1 < X 2 < X 3 Π = S T - X 1 - C 1 + 2C 2 - C 3 if X 1 < S T X 2 < X 3 Π = -S T +2X 2 - X 1 - C 1 + 2C 2 - C 3 if X 1 < X 2 < S T X 3 Π = -X 1 + 2X 2 - X 3 - C 1 + 2C 2 - C 3 if X 1 < X 2 < X 3 < S T Maximum profit = X 2 - X 1 - C 1 + 2C 2 - C 3, minimum = -C 1 + 2C 2 - C 3 Breakeven: S T* = X 1 + C 1-2C 2 + C 3 and S T * = 2X 2 - X 1 - C 1 + 2C 2 - C 3 X 1 X 2 X 3 S T X 1 X 2 X 3 S T 15 16

Butterfly Spreads (continued) A butterfly spread has a limited loss, which occurs on large stock moves, either up or down, and a limited gain, which occurs if the sock price ends up at the middle

The butterfly spread is considered low-risk strategy in that its loss is limited. The butterfly spread strategy assumes that the stock price will fluctuate very little.

5 Butterfly Spreads (continued) A butterfly spread has a limited loss, which occurs on large stock moves, either up or down, and a limited gain, which occurs if the sock price ends up at the middle exercise price. A butterfly spread has a limited loss, which occurs on large stock moves, either up or down, and a limited gain, which occurs if the sock price ends up at the middle exercise price. The butterfly spread is considered low-risk strategy in that its loss is limited. The butterfly spread strategy assumes that the stock price will fluctuate very little. Thus the butterfly spread strategy is one of the volatility strategies because it is based on the expectation of high or low volatility rather than the direction of the stock. See Figure 7.7 for DCRB July 120/125/130, C1 = $16.00, C2 = $13.50, C3 = $ Straddles Straddles Straddle: long an equal number of puts and calls Profit equation: Π = Max(0,S T - X) - C + Max(0,X - S T ) - P (assuming N c = 1, N p = 1) Π = S T - X - C - P if S T X Π = X - S T - C - P if S T < X Breakeven: S T* = X - C - P and S T* = X + C + P Maximum profit:, minimum = - C P. See Figure 7.11 for DCRB June 125, C = $13.50, P = $ The profit potential on a straddle is unlimited. However, we should be aware that the straddle normally requires a fairly large stock price move to be profitable. From Figure 7.11, it would require about a 20% increase or decrease in the stock price in one month to make a profit. A straddle is a strategy designed to profit if there is a large up or down move in the stock. If S T X, then Π = S T If S T < X, then Π = S T Breakeven: S T* = 100 and S T * = 150 Maximum profit:, minimum =

6 Straddles (continued) Applications of Straddles Appropriate for situations in which one suspect that the stock price will move substantially but does not know in which direction it will go. Based on perception of volatility greater than priced by market A Short Straddle Expects the market to stay within a narrow trading range. Unlimited loss potential Based on perception of volatility less than priced by market 21

Using Position in an Option & the Underlying

Using Position in an Option & the Underlying Week 8 : Strategies Introduction Assume that the underlying asset is a stock paying no income Assume that the options are EUROPEAN Ignore time value of money In figures o Dashed line relationship between