Chapter 6: Basic Option Strategies A good trader with a bad model can beat a bad trader with a good...

Chapter 6: Basic Option Chapter 6: Basic Option StrategiesStrategies

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/BrooksAn Introduction to Derivatives and Risk Management, 9th ed.

Ch. 6: 1

© 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.

Important Concepts in Chapter 6Important Concepts in Chapter 6Profit 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


Ch. 6: 2


Terminology and NotationTerminology and NotationNote 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◦ = 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


Ch. 6: 3


Terminology and Notation (continued)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

= NC[Max(0,ST - X) - C] For buyer of one call (NC = 1) this implies = Max(0,ST -

X) - C For seller of one call (NC = -1) this implies =

-Max(0,ST - X) + C


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The Profit Equations (continued)◦Profit equation for puts held to expiration

= NP[Max(0,X - ST) - P] For buyer of one put (NP = 1) this implies = Max(0,X -

ST) - P

For seller of one put (NP = -1) this implies = -Max(0,X - ST) + P


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The Profit Equations (continued)◦Profit equation for stock

= NS[ST - S0] For buyer of one share (NS = 1) this implies = ST - S0

For short seller of one share (NS = -1) this implies = -ST + S0


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Terminology and Notation Terminology and Notation (continued)(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.


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Terminology and Notation Terminology and Notation (continued)(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.


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Stock TransactionsStock TransactionsBuy Stock◦Profit equation: = 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: = NS[ST - S0] given that NS

< 0◦See Figure 6.2 for DCRB, S0 = $125.94◦Maximum profit = S0, minimum = -


Ch. 6: 9


Call Option TransactionsCall Option TransactionsBuy a Call◦Profit equation: = NC[Max(0,ST - X) - C]

given that NC > 0. Letting NC = 1, = ST - X - C if ST > X

= - 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


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Call Option Transactions Call Option Transactions (continued)(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.


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Call Option Transactions Call Option Transactions (continued)(continued)Write a Call◦Profit equation: = NC[Max(0,ST - X) - C]

given that NC < 0. Letting NC = -1, = -ST + X + C if ST > X

= 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


Ch. 6: 12


Call Option Transactions Call Option Transactions (continued)(continued)Write a Call (continued)◦See Figure 6.7 for different exercise prices.


◦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.



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Call Option Transactions Call Option Transactions (continued)(continued)

14) Buy one August 165 call contract at C = 5.25. 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?


Ch. 6: 14


Put Option TransactionsPut Option TransactionsBuy a Put◦Profit equation: = NP[Max(0,X - ST) - P]

given that NP > 0. Letting NP = 1, = X - ST - P if ST < X

= - P if ST 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


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Put Option Transactions (continued)Put Option Transactions (continued)

Buy a Put (continued)◦See Figure 6.10 for different exercise prices.





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Write a Put◦Profit equation: = NP[Max(0,X - ST)- P]

given that NP < 0. Letting NP = -1 = -X + ST + P if ST < X

= P if ST 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


Ch. 6: 17



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.


Figure 6.15 summarizes these payoff graphs.


Ch. 6: 18



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.


Ch. 6: 19


Calls and Stock: the Covered CallCalls and Stock: the Covered Call

◦One short call for every share owned◦Profit equation: = NS(ST - S0) + NC[Max(0,ST - X) -

C] given NS > 0, NC < 0, NS = -NC. With NS = 1, NC = -1, = ST - S0 + C if ST X = 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


Ch. 6: 20


Calls and Stock: the Covered Call Calls and Stock: the Covered Call (continued)(continued)

◦See Figure 6.17 for different exercise prices. Note differences in maximum loss and breakeven.


◦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


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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.


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18) A call option on the euro expiring in six months has an exercise price of $1.00 and is priced at $0.0385. Construct a euro covered call. Assume that the spot rate at the start is $0.9825.


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Puts and Stock: the Protective PutPuts and Stock: the Protective Put

◦ One long put for every share owned

◦ Profit equation: = NS(ST - S0) + NP[Max(0,X - ST) - P] given NS > 0, NP > 0, NS = NP. With NS = 1, NP = 1,

= ST - S0 - P if ST X = 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


Ch. 6: 24


Puts and Stock: the Protective Put Puts and Stock: the Protective Put (continued)(continued)

◦See Figure 6.20 for different exercise prices. Note differences in maximum loss and breakeven.




Ch. 6: 25



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


Ch. 6: 26



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.


Ch. 6: 27


Synthetic Puts and CallsSynthetic 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.


Ch. 6: 28


Synthetic Puts and Calls (continued)Synthetic Puts and Calls (continued)◦Profit equation: = NC[Max(0,ST - X) - C]

+ NS(ST - S0) given that NC > 0, NS < 0, NS = NP. Letting NC = 1, NS = -1, = -C - ST + S0 if ST X = 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.


Ch. 6: 29


Synthetic Puts and Calls (continued)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.


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My ProblemsMy 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


Ch. 6: 56


TAProblemsTAProblems◦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)


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