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Chapter 6: Basic Option Strategies

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Chapter 6: Basic Option Strategies With derivative products and options you can pick any point of the payoff distribution and sell off all the others. Stan Jonas Derivatives Strategy , November, 1995, p. 66 Important Concepts

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### Chapter 6: Basic Option Strategies

With derivative products and options you can pick any point of the payoff distribution and sell off all the others.

Stan Jonas

Derivatives Strategy, November, 1995, p. 66

An Introduction to Derivatives and Risk Management, 7th ed.

Important Concepts

- 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

An Introduction to Derivatives and Risk Management, 7th ed.

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

An Introduction to Derivatives and Risk Management, 7th ed.

Terminology and Notation (continued)

- These symbols imply the following:
- NC,NP, or NS > 0 implies buying (long position)
- NC, NP, or NS < 0 implies selling (short position)

- 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

- P = NC[Max(0,ST - X) - C]

- Profit equation for calls held to expiration

An Introduction to Derivatives and Risk Management, 7th ed.

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

- P = NP[Max(0,X - ST) - P]

- Profit equation for puts held to expiration

An Introduction to Derivatives and Risk Management, 7th ed.

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)

- P = NS[ST - S0]

- Profit equation for stock

An Introduction to Derivatives and Risk Management, 7th ed.

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.

An Introduction to Derivatives and Risk Management, 7th ed.

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, p. 197.

An Introduction to Derivatives and Risk Management, 7th ed.

Stock Transactions

- Buy Stock
- Profit equation: P = NS[ST - S0] given that NS > 0
- See Figure 6.1, p. 186 for DCRB, S0 = $125.94, NS = 100
- Maximum profit = , minimum = -S0

- Sell Short Stock
- Profit equation: P = NS[ST - S0] given that NS < 0
- See Figure 6.2, p. 186 for DCRB, S0 = $125.94, NS = -100
- Maximum profit = S0, minimum = -

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Buying Stock

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Selling Stock Short

An Introduction to Derivatives and Risk Management, 7th ed.

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, p. 188 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 = $125 + $13.50 = $138.50

- Profit equation: P = NC[Max(0,ST - X) - C] given that NC > 0. Letting NC = 1,

An Introduction to Derivatives and Risk Management, 7th ed.

Call Option Transactions (continued)

- Buy a Call (continued)
- See Figure 6.4, p. 189 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, p. 190 and Figure 6.5, p. 190.
- June 4: P = 100($7.16 - $18.60) = - $1,144

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

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Buying Call

An Introduction to Derivatives and Risk Management, 7th ed.

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, p. 192 for DCRB June 125, C = $13.50
- Maximum profit = +C, minimum = -
- Breakeven stock price same as buying call: ST* = X + C = $125 + $13.50 = $138.50

- Profit equation: P = NC[Max(0,ST - X) - C] given that NC < 0. Letting NC = -1,

An Introduction to Derivatives and Risk Management, 7th ed.

Call Option Transactions (continued)

- Write a Call (continued)
- See Figure 6.7, p. 192 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, p. 193.
- Note how time value decay affects profit for given holding period.

An Introduction to Derivatives and Risk Management, 7th ed.

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 ST³ X

- See Figure 6.9, p. 194 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 = $125 - $11.50 = $113.50

- Profit equation: P = NP[Max(0,X - ST) - P] given that NP > 0. Letting NP = 1,

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Buying Put

An Introduction to Derivatives and Risk Management, 7th ed.

Put Option Transactions (continued)

- Buy a Put (continued)
- See Figure 6.10, p. 195 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 6.11, p. 196.
- Note how time value decay affects profit for given holding period.

An Introduction to Derivatives and Risk Management, 7th ed.

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 ST³ X

- See Figure 6.12, p. 197 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 = $125 - $11.50 = $113.50

- Profit equation: P = NP[Max(0,X - ST)- P] given that NP < 0. Letting NP = -1

An Introduction to Derivatives and Risk Management, 7th ed.

Put Option Transactions (continued)

- Write a Put (continued)
- See Figure 6.13, p. 197 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, p. 198.
- Note how time value decay affects profit for given holding period.

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

An Introduction to Derivatives and Risk Management, 7th ed.

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, p. 201 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 = $125.94 - $13.50 = $112.44

An Introduction to Derivatives and Risk Management, 7th ed.

Calls and Stock: the Covered Call (continued)

- See Figure 6.17, p. 202 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, p. 203.
- Note the effect of time value decay.
- Some General Considerations for Covered Calls:
- alleged attractiveness of the strategy
- misconception about picking up income
- rolling up to avoid exercise

- Opposite is short stock, buy call

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Covered Call Position

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Covered Call Position

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Partially Covered Call

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from 2:1 Ratio Write Strategy

An Introduction to Derivatives and Risk Management, 7th ed.

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 ST³ X
- P = X - S0 - P if ST < X

- See Figure 6.19, p. 205 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 = $11.50 + $125.94 = $137.44
- Like insurance policy

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Protective Put

An Introduction to Derivatives and Risk Management, 7th ed.

Puts and Stock: the Protective Put (continued)

- See Figure 6.20, p. 206for 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, p. 207.
- Note how time value decay affects profit for given holding period.

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from Protective Put

An Introduction to Derivatives and Risk Management, 7th ed.

Profit from One Put for Two Shares

An Introduction to Derivatives and Risk Management, 7th ed.

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.

An Introduction to Derivatives and Risk Management, 7th ed.

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, p. 210 for synthetic put vs. actual put.
- Reverse Conversion or Reversal
- P + S0 = C + Xe-rcT
- -Xe-rcT = C – P – S0

- Table 6.3, p. 211 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.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

An Introduction to Derivatives and Risk Management, 7th ed.

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