basic option strategies

Basic Option Strategies

Week no 10

Important Concepts

Profit equations and graphs for buying and selling stock, Profit equations and graphs for buying and selling stock, buying and selling calls, buying and selling puts, covered buying and selling calls, buying and selling puts, covered calls, protective putscalls, protective puts

The effect of choosing different exercise pricesThe effect of choosing different exercise prices The effect of closing out an option position early versus The effect of closing out an option position early versus

holding to expirationholding to expiration

Terminology and Notation Note the following standard symbolsNote the following standard symbols

C = current call price, P = current put priceC = current call price, P = current put price SS00 = current stock price, S = current stock price, STT = stock price at expiration = stock price at expiration T = time to expirationT = time to expiration X = exercise priceX = exercise price = profit from strategy

The number of calls, puts and stock is given asThe number of calls, puts and stock is given as NNCC = number of calls = number of calls NNPP = number of puts = number of puts NNSS = number of shares of stock = number of shares of stock

Terminology and Notation (continued) These symbols imply the following:These symbols imply the following:

NNCC,, NNPP,, or N or NSS > 0 implies buying (going long) > 0 implies buying (going long) NNCC, N, NPP, or N, or NSS < 0 implies selling (going short) < 0 implies selling (going short)

The Profit EquationsThe Profit Equations Profit equation for calls held to expirationProfit equation for calls held to expiration

= N= NCC[Max(0,S[Max(0,STT - X) - C] - X) - C]• For buyer of one call (NFor buyer of one call (NCC = 1) this implies = 1) this implies

= Max(0,S= Max(0,STT - X) - C - X) - C• For seller of one call (NFor seller of one call (NCC = -1) this implies = -1) this implies

= -Max(0,S = -Max(0,STT - X) + C - X) + C

Terminology and Notation (continued) The Profit Equations (continued)The Profit Equations (continued)

Profit equation for puts held to expirationProfit equation for puts held to expiration = N= NPP[Max(0,X - S[Max(0,X - STT) - P]) - P]

• For buyer of one put (NFor buyer of one put (NPP = 1) this implies = 1) this implies = Max(0,X - S = Max(0,X - STT) - P) - P

• For seller of one put (NFor seller of one put (NPP = -1) this implies = -1) this implies = -Max(0,X - S = -Max(0,X - STT) + P) + P

Terminology and Notation (continued)

The Profit Equations (continued)The Profit Equations (continued) Profit equation for stockProfit equation for stock

= N= NSS[S[STT - S - S00]]

• For buyer of one share (NFor buyer of one share (NSS = 1) this implies = 1) this implies = S = STT - S - S00

• For short seller of one share (NFor short seller of one share (NSS = -1) this = -1) this implies implies = -S = -STT + S + S00


Different Holding PeriodsDifferent Holding Periods Three holding periods: TThree holding periods: T11 < T < T22 < T < T For a given stock price at the end of the holding period, compute For a given stock price at the end of the holding period, compute

the theoretical value of the option using the Black-Scholes-Merton the theoretical value of the option using the Black-Scholes-Merton or other appropriate model.or other appropriate model. Remaining time to expiration will be either T - TRemaining time to expiration will be either T - T11, ,

T - TT - T22 or T - T = 0 (we have already covered the latter) or T - T = 0 (we have already covered the latter) For a position closed out at TFor a position closed out at T11, the profit will be, the profit will be

where the closeout option price is taken from the Black-where the closeout option price is taken from the Black-Scholes-Merton model for a given stock price at TScholes-Merton model for a given stock price at T11. .

C].X),TT,[C(SN 1Tc 1


Different Holding Periods (continued)Different Holding Periods (continued) Similar calculation done for TSimilar calculation done for T22

For T, the profit is determined by the intrinsic value, as For T, the profit is determined by the intrinsic value, as already coveredalready covered

AssumptionsAssumptions No dividendsNo dividends No taxes or transaction costsNo taxes or transaction costs We continue with the DCRB options. See We continue with the DCRB options. See

Table 6.1, p. 197..

Stock Transactions

Buy StockBuy Stock Profit equation: Profit equation: = NS[ST - S0] given that NS > 0 See Figure 6.1, p. 186 for DCRB, S0 = $125.94 Maximum profit = , minimum = -S0

Sell Short StockSell Short Stock Profit equation: Profit equation: = NS[ST - S0] given that NS < 0 See Figure 6.2, p. 186 for DCRB, S0 = $125.94 Maximum profit = S0, minimum = -

Call Option Transactions

Buy a CallBuy a Call Profit equation: Profit equation: = N = NCC[Max(0,S[Max(0,STT - X) - C] given that - X) - C] given that

NNCC > 0. Letting N > 0. Letting NCC = 1, = 1, = S= STT - X - C if S - X - C if STT > X > X = - C if S= - C if STT X X

See See Figure 6.3, p. 188 for DCRB June 125, C = $13.50 for DCRB June 125, C = $13.50 Maximum profit = Maximum profit = , minimum = -C, minimum = -C Breakeven stock price found by setting profit equation Breakeven stock price found by setting profit equation

to zero and solving: Sto zero and solving: STT** = X + C = X + C

Call Option Transactions (continued)

Buy a Call (continued)Buy a Call (continued) See See Figure 6.4, p. 189 for different exercise prices. for different exercise prices.

Note differences in maximum loss and breakeven.Note differences in maximum loss and breakeven. For different holding periods, compute profit for range For different holding periods, compute profit for range

of stock prices at Tof stock prices at T11, T, T22, and T using Black-Scholes-, and T using Black-Scholes-Merton model. See Merton model. See Figure 6.5, p. 190..

Note how time value decay affects profit for given Note how time value decay affects profit for given holding period.holding period.


Write a CallWrite a Call Profit equation: Profit equation: = N = NCC[Max(0,S[Max(0,STT - X) - C] given that - X) - C] given that

NNCC < 0. Letting N < 0. Letting NCC = -1, = -1, = -S= -STT + X + C if S + X + C if STT > X > X = C if S= C if STT X X

See See Figure 6.6, p. 192 for DCRB June 125, C = $13.50 for DCRB June 125, C = $13.50 Maximum profit = +C, minimum = - Maximum profit = +C, minimum = - Breakeven stock price same as buying call: Breakeven stock price same as buying call:

SSTT** = X + C = X + C


Write a Call (continued)Write a Call (continued) See See Figure 6.7, p. 192 for different exercise prices. for different exercise prices.




Put Option Transactions

Buy a PutBuy a Put Profit equation: Profit equation: = N = NPP[Max(0,X - S[Max(0,X - STT) - P] given that ) - P] given that

NNPP > 0. Letting N > 0. Letting NPP = 1, = 1, = X - S= X - STT - P if S - P if STT < X < X = - P if S= - P if STT X X

See See Figure 6.9, p. 194 for DCRB June 125, P = $11.50 for DCRB June 125, P = $11.50 Maximum profit = X - P, minimum = -PMaximum profit = X - P, minimum = -P Breakeven stock price found by setting profit equation Breakeven stock price found by setting profit equation

to zero and solving: Sto zero and solving: STT** = X - P = X - P

Put Option Transactions (continued)

Buy a Put (continued)Buy a Put (continued) See See Figure 6.10, p. 195 for different exercise prices. for different exercise prices.





Write a PutWrite a Put Profit equation: Profit equation: = N = NPP[Max(0,X - S[Max(0,X - STT)- P] given that )- P] given that

NNPP < 0. Letting N < 0. Letting NPP = -1 = -1 = -X + S= -X + STT + P if S + P if STT < X < X = P if S= P if STT X X

See See Figure 6.12, p. 197 for DCRB June 125, P = $11.50 for DCRB June 125, P = $11.50 Maximum profit = +P, minimum = -X + PMaximum profit = +P, minimum = -X + P Breakeven stock price found by setting profit equation Breakeven stock price found by setting profit equation

to zero and solving: Sto zero and solving: STT** = X - P = X - P


Write a Put (continued)Write a Put (continued) See See Figure 6.13, p. 197 for different exercise prices. for different exercise prices.




Figure 6.15, p. 199 summarizes these payoff graphs. summarizes these payoff graphs.

Calls and Stock: the Covered Call

One short call for every share ownedOne short call for every share owned Profit equation: Profit equation: = N = NSS(S(STT - S - S00) + N) + NCC[Max(0,S[Max(0,STT - X) - C] - X) - C]

given Ngiven NSS > 0, N > 0, NCC < 0, N < 0, NSS = -N = -NCC. With N. With NSS = 1, N = 1, NCC = -1, = -1, = S= STT - S - S00 + C if S + C if STT X X = X - S= X - S00 + C if S + C if STT > X > X

See See Figure 6.16, p. 201 for DCRB June 125, for DCRB June 125, SS00 = $125.94, C = $13.50 = $125.94, C = $13.50

Maximum profit = X - SMaximum profit = X - S00 + C, minimum = -S + C, minimum = -S00 + C + C Breakeven stock price found by setting profit equation to Breakeven stock price found by setting profit equation to

zero and solving: Szero and solving: STT** = S = S00 - C - C

Calls and Stock: the Covered Call (continued)

See See Figure 6.17, p. 202 for different exercise prices. for different exercise prices. Note differences in maximum loss and breakeven.Note differences in maximum loss and breakeven.

For different holding periods, compute profit for range For different holding periods, compute profit for range of stock prices at Tof stock prices at T11, T, T22, and T using Black-Scholes-, and T using Black-Scholes-Merton model. See Merton model. See Figure 6.18, p. 203..

Note the effect of time value decay.Note the effect of time value decay. Some General Considerations for Covered Calls: Some General Considerations for Covered Calls:

alleged attractiveness of the strategyalleged attractiveness of the strategy misconception about picking up incomemisconception about picking up income rolling up to avoid exerciserolling up to avoid exercise

Opposite is short stock, buy callOpposite is short stock, buy call

Puts and Stock: the Protective Put One long put for every share ownedOne long put for every share owned Profit equation: Profit equation: = N = NSS(S(STT - S - S00) + N) + NPP[Max(0,X - S[Max(0,X - STT) - P] given ) - P] given

NNSS > 0, N > 0, NPP > 0, N > 0, NSS = N = NPP. With N. With NSS = 1, N = 1, NPP = 1, = 1, = S= STT - S - S00 - P if S - P if STT XX = X - S= X - S00 - P if S - P if STT < X < X

See See Figure 6.19, p. 205 for DCRB June 125, S for DCRB June 125, S00 = $125.94, = $125.94, P = $11.50P = $11.50

Maximum profit = Maximum profit = , minimum = X - S, minimum = X - S00 - P - P Breakeven stock price found by setting profit equation to zero and Breakeven stock price found by setting profit equation to zero and

solving: Ssolving: STT** = P + S = P + S00

Puts and Stock: the Protective Put (continued)

See See Figure 6.20, p. 206 for different exercise prices. for different exercise prices. Note differences in maximum loss and breakeven.Note differences in maximum loss and breakeven.

For different holding periods, compute profit for range For different holding periods, compute profit for range of stock prices at Tof stock prices at T11, T, T22, and T using Black-Scholes-, and T using Black-Scholes-Merton model. See Merton model. See Figure 6.21, p. 207..


Synthetic Puts and Calls Rearranging put-call parity to isolate put priceRearranging put-call parity to isolate put price

This implies put = long call, short stock, long risk-free This implies put = long call, short stock, long risk-free bond with face value X.bond with face value X.

This is a synthetic put.This is a synthetic put. In practice most synthetic puts are constructed without In practice most synthetic puts are constructed without

risk-free bond, i.e., long call, short stock. risk-free bond, i.e., long call, short stock.

Tr0

cXeSCP

Synthetic Puts and Calls (continued) Profit equation: Profit equation: = N = NCC[Max(0,S[Max(0,STT - X) - C] - X) - C]

+ N+ NSS(S(STT - S - S00) given that N) given that NCC > 0, N > 0, NSS < 0, N < 0, NSS = N = NPP. Letting . Letting NNCC = 1, N = 1, NSS = -1, = -1, = -C - S= -C - STT + S + S00 if S if STT XX = S= S00 - X - C if S - X - C if STT > X > X

See See Figure 6.22, p. 210 for synthetic put vs. actual put. for synthetic put vs. actual put. Table 6.3, p. 211 shows payoffs from reverse conversion shows payoffs from reverse conversion

(long call, short stock, short put), used when actual put is (long call, short stock, short put), used when actual put is overpriced. Like risk-free borrowing.overpriced. Like risk-free borrowing.

Similar strategy for conversion, used when actual call Similar strategy for conversion, used when actual call overpriced.overpriced.

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basic option strategies

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