1. Chapter 6: Basic Option Strategies
A good trader with a bad model can beat a bad trader with a good model.
William Margrabe
Derivatives Strategy, April, 1998, p. 27
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

2. Important Concepts in Chapter 6
Profit equations and graphs for buying and selling stock, buying and selling calls, buying and selling puts, covered calls, protective puts and conversions/reversals
The effect of choosing different exercise prices
The effect of closing out an option position early versus holding to expiration
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

3. Terminology and Notation
Note the following standard symbols
C = current call price, P = current put price
S0 = current stock price, ST = stock price at expiration
T = time to expiration
X = exercise price
P = profit from strategy
The number of calls, puts and stock is given as
NC = number of calls
NP = number of puts
NS = number of shares of stock
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

4. Terminology and Notation (continued)
These symbols imply the following:
NC, NP, or NS > 0 implies buying (going long)
NC, NP, or NS < 0 implies selling (going short)
The Profit Equations
Profit equation for calls held to expiration
P = NC[Max(0,ST - X) - C]
For buyer of one call (NC = 1) this implies P = Max(0,ST - X) - C
For seller of one call (NC = -1) this implies P = -Max(0,ST - X) + C
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

5. Terminology and Notation (continued)
The Profit Equations (continued)
Profit equation for puts held to expiration
P = NP[Max(0,X - ST) - P]
For buyer of one put (NP = 1) this implies P = Max(0,X - ST) - P
For seller of one put (NP = -1) this implies P = -Max(0,X - ST) + P
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

6. Terminology and Notation (continued)
The Profit Equations (continued)
Profit equation for stock
P = NS[ST - S0]
For buyer of one share (NS = 1) this implies P = ST - S0
For short seller of one share (NS = -1) this implies P = -ST + S0
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

7. Terminology and Notation (continued)
Different Holding Periods
Three holding periods: T1 < T2 < T
For a given stock price at the end of the holding period, compute the theoretical value of the option using the Black-Scholes-Merton or other appropriate model.
Remaining time to expiration will be either T - T1, T - T2 or T - T = 0 (we have already covered the latter)
For a position closed out at T1, the profit will be
where the closeout option price is taken from the Black-Scholes-Merton model for a given stock price at T1.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

8. Terminology and Notation (continued)
Different Holding Periods (continued)
Similar calculation done for T2
For T, the profit is determined by the intrinsic value, as already covered
Assumptions
No dividends
No taxes or transaction costs
We continue with the DCRB options. See Table 6.1.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

9. Stock Transactions Buy Stock Sell Short Stock
Profit equation: P = NS[ST - S0] given that NS > 0
See Figure 6.1 for DCRB, S0 = $125.94
Maximum profit = , minimum = -S0
Sell Short Stock
Profit equation: P = NS[ST - S0] given that NS < 0
See Figure 6.2 for DCRB, S0 = $125.94
Maximum profit = S0, minimum = - 
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

10. Call Option Transactions
Buy a Call
Profit equation: P = NC[Max(0,ST - X) - C] given that NC > 0. Letting NC = 1,
P = ST - X - C if ST > X
P = - C if ST £ X
See Figure 6.3 for DCRB June 125, C = $13.50
Maximum profit = , minimum = -C
Breakeven stock price found by setting profit equation to zero and solving: ST* = X + C
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

11. Call Option Transactions (continued)
Buy a Call (continued)
See Figure 6.4 for different exercise prices. Note differences in maximum loss and breakeven.
For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Table 6.2 and Figure 6.5.
Note how time value decay affects profit for given holding period.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

12. Call Option Transactions (continued)
Write a Call
Profit equation: P = NC[Max(0,ST - X) - C] given that NC < 0. Letting NC = -1,
P = -ST + X + C if ST > X
P = C if ST £ X
See Figure 6.6 for DCRB June 125, C = $13.50
Maximum profit = +C, minimum = - 
Breakeven stock price same as buying call: ST* = X + C
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

13. Call Option Transactions (continued)
Write a Call (continued)
See Figure 6.7 for different exercise prices. Note differences in maximum loss and breakeven.
For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 6.8.
Note how time value decay affects profit for given holding period.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

14. Call Option Transactions (continued)
14) Buy one August 165 call contract at C = Hold it until the options expire. Determine the profits and graph the results. Then identify the breakeven stock price at expiration. What is the maximum possible loss on this transaction?
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

15. Put Option Transactions
Buy a Put
Profit equation: P = NP[Max(0,X - ST) - P] given that NP > 0. Letting NP = 1,
P = X - ST - P if ST < X
P = - P if ST ³ X
See Figure 6.9 for DCRB June 125, P = $11.50
Maximum profit = X - P, minimum = -P
Breakeven stock price found by setting profit equation to zero and solving: ST* = X - P
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

16. Put Option Transactions (continued)
Buy a Put (continued)
See Figure 6.10 for different exercise prices. Note differences in maximum loss and breakeven.
For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure
Note how time value decay affects profit for given holding period.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

17. Put Option Transactions (continued)
Write a Put
Profit equation: P = NP[Max(0,X - ST)- P] given that NP < 0. Letting NP = -1
P = -X + ST + P if ST < X
P = P if ST ³ X
See Figure 6.12 for DCRB June 125, P = $11.50
Maximum profit = +P, minimum = -X + P
Breakeven stock price found by setting profit equation to zero and solving: ST* = X - P
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

18. Put Option Transactions (continued)
Write a Put (continued)
See Figure 6.13 for different exercise prices. Note differences in maximum loss and breakeven.
For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black- Scholes-Merton model. See Figure 6.14.
Note how time value decay affects profit for given holding period.
Figure 6.15 summarizes these payoff graphs.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

19. Put Option Transactions (continued)
7) Buying an at-the-money put has a greater return potential than buying an out-of-the- money put because it is more likely to be in- the-money. Appraise this statement.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

20. Calls and Stock: the Covered Call
One short call for every share owned
Profit equation: P = NS(ST - S0) + NC[Max(0,ST - X) - C] given NS > 0, NC < 0, NS = -NC. With NS = 1, NC = -1,
P = ST - S0 + C if ST £ X
P = X - S0 + C if ST > X
See Figure 6.16 for DCRB June 125, S0 = $125.94, C = $13.50
Maximum profit = X - S0 + C, minimum = -S0 + C
Breakeven stock price found by setting profit equation to zero and solving: ST* = S0 - C
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

21. Calls and Stock: the Covered Call (continued)
See Figure 6.17 for different exercise prices. Note differences in maximum loss and breakeven.
For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black- Scholes-Merton model. See Figure 6.18.
Note the effect of time value decay.
Some General Considerations for Covered Calls:
misconception about picking up income
rolling up to avoid exercise
Opposite is short stock, buy call
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

22. Calls and Stock: the Covered Call (continued)
8) A short position in stock can be protected by holding a call option. Determine the profit equations for this position and identify the breakeven stock price at expiration and maximum and minimum profits.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

23. Calls and Stock: the Covered Call (continued)
18) A call option on the euro expiring in six months has an exercise price of $1.00 and is priced at $ Construct a euro covered call. Assume that the spot rate at the start is $
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

24. Puts and Stock: the Protective Put
One long put for every share owned
Profit equation: P = NS(ST - S0) + NP[Max(0,X - ST) - P] given NS > 0, NP > 0, NS = NP. With NS = 1, NP = 1,
P = ST - S0 - P if ST ³ X
P = X - S0 - P if ST < X
See Figure 6.19 for DCRB June 125, S0 = $125.94, P = $11.50
Maximum profit = , minimum = X - S0 - P
Breakeven stock price found by setting profit equation to zero and solving: ST* = P + S0
Like insurance policy
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

25. Puts and Stock: the Protective Put (continued)
See Figure 6.20 for different exercise prices. Note differences in maximum loss and breakeven.
For different holding periods, compute profit for range of stock prices at T1, T2, and T using Black-Scholes-Merton model. See Figure 6.21.
Note how time value decay affects profit for given holding period.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

26. Puts and Stock: the Protective Put (continued)
23) Another consideration in evaluating option strategies is the effect of transaction costs. Suppose that purchases and sales of an option incur a brokerage commission of 1 percent of the option’s value. Purchases and sales of a share of stock incur a brokerage commission of 0.5 percent of the stock’s value. If the option is exercised, there is a transaction cost on the purchase or sale of the stock. Determine the profit equations for the following strategies assuming that the options are held to expiration and exercised if in-the-money rather than sold back. Assume that one option and/or share is used and that any shares left in the portfolio are sold. a. Long call b. Long put c. Covered call d. Protective put
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

27. Puts and Stock: the Protective Put (continued)
20) The Black-Scholes-Merton option pricing model assumes that stock price changes are lognormally distributed. Show graphically how this distribution changes when an investor is long the stock and long the put.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

28. Synthetic Puts and Calls
Rearranging put-call parity to isolate put price
This implies put = long call, short stock, long risk-free bond with face value X.
This is a synthetic put.
In practice most synthetic puts are constructed without risk-free bond, i.e., long call, short stock.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

29. Synthetic Puts and Calls (continued)
Profit equation: P = NC[Max(0,ST - X) - C] + NS(ST - S0) given that NC > 0, NS < 0, NS = NP. Letting NC = 1, NS = -1,
P = -C - ST + S0 if ST £ X
P = S0 - X - C if ST > X
See Figure 6.22 for synthetic put vs. actual put.
Table 6.3 shows payoffs from reverse conversion (long call, short stock, short put), used when actual put is overpriced. Like risk-free borrowing.
Similar strategy for conversion, used when actual call overpriced.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

30. Synthetic Puts and Calls (continued)
22) Compute the call and put prices for a stock option, where the current stock price is $100, the exercise price is $100, the risk-free interest rate is 5 percent (continuously compounded), the volatility is 30 percent, and the time to expiration is one year. Explain how you would create a synthetic call option and identify the cost.
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

31. (Return to text slide)
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

32. (Return to text slide)
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

33. (Return to text slide)
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

34. (Return to text slide)
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

35. (Return to text slide)
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

36. (Return to text slide)
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

37. (Return to text slide)
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

38. (Return to text slide)
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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An Introduction to Derivatives and Risk Management, 9th ed.
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An Introduction to Derivatives and Risk Management, 9th ed.
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56. My Problems 7 Buy a put, choice of exercise price
8 The Opposite of Covered Call
14 Buy a Call
18 The Covered Call
20 The Protective Put
22 Synthetic Calls & Puts (conversion)
23 Effect of Transaction Costs
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

57. TAProblems 6 Buy a Put 9 Synthetic Calls & Puts (conversion)
11 The Covered Call (Using Excel)
16 Buy a Call
19 Synthetic Calls & Puts
21 The Covered Call
25 Synthetic Calls & Puts (reverse conversion)
Chance/Brooks
An Introduction to Derivatives and Risk Management, 9th ed.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.