Options_trading strategies
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Profit
X1
X2
ST
Spreads - Bear Spread (1)
• Bear Spread: Buy 1 call option & sell 1 call option with lower strike price. Maturity is the same. Underlying asset is the same. Strike price: X2 < X1. Assumption: E0(ST) . Positive cash flow at time 0. • Again, bear spreads limit both potential profits and losses.
Spreads - Bull Spread (4)
• Bull spread using puts: Buy 1 put option & sell 1 put option with higher strike price. Maturity is the same. Underlying asset is the same. Strike prices: X1 < X2 ==> Positive cash flow at time 0 (it was negative with a call spread) & final payoffs lower than those created using calls. Assumption: E0(ST) .
Note: these are payoffs (not profits). They do not include the actual cost of the options as in the graph.
Spreads - Butterfly Spread (3)
• Butterfly Spread using puts: Buy 1 put option with low strike price (X1), buy 1 put option with high strike price (X3) and sell 2 put options with a strike price (X2) halfway between X1 and X3. • Assumption: E0(ST) S0 (low volatility). Put-call parity can be used to show that the initial investment is the same as for a spread with calls.
From put-call parity: a protective put is like a call + money (see graph)
• p + S = c + e-rTX ==> S - c = - p + M where M = e-rTX, M is money
From put-call parity: a covered call is like a short put + money (see graph)
Note: these are payoffs (not profits). They do not include the actual cost of the options (negative here) as in the graph.
Spreads - Bear Spread (3)
• Bear spread using puts: Buy 1 put option & sell 1 put option with lower strike price. Maturity is the same. Underlying asset is the same. Strike price: X2 < X1. Assumption: E0(ST) . Negative cash flow at time 0.
Profit X1
X2
ST
Spreads - Bull Spread (2)
Stock Price ST X2 X 1 < ST < X 2 ST X1 Payoff from long Call ST - X1 ST - X1 0 Payoff from short Call X 2 - ST 0 0 Total Payoff X 2 – X1 ST - X1 0
Long stock
Profit
Profit
X
Long call
X
ST Important: on this axis we have the stock price at expiration of the option
Short call Short stock
ST
Covered call
Payoff from call
Note: these are payoffs (not profits). They do not include the actual cost of the options as in the graphs.
Spreads - Bull Spread (3)
• Bull spreads limit both the investor’s profits and losses. The investor gives up some of the upside potential profits from the long position and, in return, reduces the initial investment (= difference in price between the two options).
Pr- Bear Spread (2)
Stock Price ST X1 X 2 < ST < X 1 ST X2 Payoff from long Call ST - X1 0 0 Payoff from short Call X2 - ST X2 - ST 0 Total Payoff - (X1 – X2) - (ST – X2) 0
Profit
X1
X2
X3
ST
Spreads - Butterfly Spread (2)
• We are assuming that: X2 = (X1 + X3)/2.
Stock Price ST X1 X 1 < ST X 2 X 2 < ST X 3 ST > X 3 Payoff 1st call 0 ST - X 1 ST - X 1 ST - X 1 Payoff 2nd call 0 0 0 ST - X 3 Payoff short calls 0 0 - 2(ST - X2) - 2(ST - X2) Total Payoff 0 ST - X 1 X 3 – ST 0
Profit
X1 X2 ST
Spreads - Butterfly Spread (1)
• Butterfly Spread: Buy 1 call option with low strike price (X1), buy 1 call option with high strike price (X3) and sell 2 call options with a strike price (X2) halfway between X1 and X3: generally X2 is close to the current stock market price. Assumption: E0(ST) S0 (low volatility).
• Three types of bull spreads:
• both option are out of the money (aggressive strategy, low cost & low probability of high payoff) • One call in the money, the other call out of the money • Both in the money (conservative).
Trading Strategies Involving Two Options (Same Type):
Spreads - Bull Spread (1) • Bull Spread: Buy 1 call option & sell 1 call option with higher strike price. Maturity is the same. Underlying asset is the same. Strike prices: X1 < X2. Assumption: E0(ST) .
Short put
Profit
X
ST
Long put
X
ST
Short stock
Protective put
Payoff from put
ST > X 0
Payoff Total from stock payoff
ST ST
Total profit
ST - cost = ST - St - p X - cost = X - St - p
ST >X -(ST - X)
Payoff Total from stock payoff
ST X
Total profit
X - cost = X – St + c ST - cost = ST – St + c
ST <X
0
ST
ST
There is a “plus” because we are selling the option
ST < X
X - ST
ST
X
Trading Strategies Involving a Single Option and a Stock (3)
Put-Call Parity: • p + S = c + e-rTX ==> p + S = c + M where M = e-rTX, M is money.
Options: Trading Strategies
Three Famous Strategies
• Take a position in the option and in the underlying (these strategies replicate other options) • Take a position in 2 or more options of the same type (Spreads) • Take a position in a mixture of calls & puts (Combinations)
Profit
X1 X2
X3
ST
Trading Strategies Involving Two Options (Different Types): Straddle (1)
• Straddle: Buy 1 call and 1 put. Same strike price and maturity. If the price of the underlying asset does not move too much (from X) ==> loss. If the price moves ==> profits.
Trading Strategies Involving a Single Option and a Stock: Profit Functions (1)
• Writing a covered call: Long in the stock & short in the call. • Reverse of writing a covered call: Short in the stock & long call.
Trading Strategies Involving a Single Option and a Stock: Profit Functions (2)
• Protective put: Long stock & long put.
Long stock
• Reverse of protective put: Short in the stock & short put. Profit
X1
X2
ST
Spreads - Bear Spread (1)
• Bear Spread: Buy 1 call option & sell 1 call option with lower strike price. Maturity is the same. Underlying asset is the same. Strike price: X2 < X1. Assumption: E0(ST) . Positive cash flow at time 0. • Again, bear spreads limit both potential profits and losses.
Spreads - Bull Spread (4)
• Bull spread using puts: Buy 1 put option & sell 1 put option with higher strike price. Maturity is the same. Underlying asset is the same. Strike prices: X1 < X2 ==> Positive cash flow at time 0 (it was negative with a call spread) & final payoffs lower than those created using calls. Assumption: E0(ST) .
Note: these are payoffs (not profits). They do not include the actual cost of the options as in the graph.
Spreads - Butterfly Spread (3)
• Butterfly Spread using puts: Buy 1 put option with low strike price (X1), buy 1 put option with high strike price (X3) and sell 2 put options with a strike price (X2) halfway between X1 and X3. • Assumption: E0(ST) S0 (low volatility). Put-call parity can be used to show that the initial investment is the same as for a spread with calls.
From put-call parity: a protective put is like a call + money (see graph)
• p + S = c + e-rTX ==> S - c = - p + M where M = e-rTX, M is money
From put-call parity: a covered call is like a short put + money (see graph)
Note: these are payoffs (not profits). They do not include the actual cost of the options (negative here) as in the graph.
Spreads - Bear Spread (3)
• Bear spread using puts: Buy 1 put option & sell 1 put option with lower strike price. Maturity is the same. Underlying asset is the same. Strike price: X2 < X1. Assumption: E0(ST) . Negative cash flow at time 0.
Profit X1
X2
ST
Spreads - Bull Spread (2)
Stock Price ST X2 X 1 < ST < X 2 ST X1 Payoff from long Call ST - X1 ST - X1 0 Payoff from short Call X 2 - ST 0 0 Total Payoff X 2 – X1 ST - X1 0
Long stock
Profit
Profit
X
Long call
X
ST Important: on this axis we have the stock price at expiration of the option
Short call Short stock
ST
Covered call
Payoff from call
Note: these are payoffs (not profits). They do not include the actual cost of the options as in the graphs.
Spreads - Bull Spread (3)
• Bull spreads limit both the investor’s profits and losses. The investor gives up some of the upside potential profits from the long position and, in return, reduces the initial investment (= difference in price between the two options).
Pr- Bear Spread (2)
Stock Price ST X1 X 2 < ST < X 1 ST X2 Payoff from long Call ST - X1 0 0 Payoff from short Call X2 - ST X2 - ST 0 Total Payoff - (X1 – X2) - (ST – X2) 0
Profit
X1
X2
X3
ST
Spreads - Butterfly Spread (2)
• We are assuming that: X2 = (X1 + X3)/2.
Stock Price ST X1 X 1 < ST X 2 X 2 < ST X 3 ST > X 3 Payoff 1st call 0 ST - X 1 ST - X 1 ST - X 1 Payoff 2nd call 0 0 0 ST - X 3 Payoff short calls 0 0 - 2(ST - X2) - 2(ST - X2) Total Payoff 0 ST - X 1 X 3 – ST 0
Profit
X1 X2 ST
Spreads - Butterfly Spread (1)
• Butterfly Spread: Buy 1 call option with low strike price (X1), buy 1 call option with high strike price (X3) and sell 2 call options with a strike price (X2) halfway between X1 and X3: generally X2 is close to the current stock market price. Assumption: E0(ST) S0 (low volatility).
• Three types of bull spreads:
• both option are out of the money (aggressive strategy, low cost & low probability of high payoff) • One call in the money, the other call out of the money • Both in the money (conservative).
Trading Strategies Involving Two Options (Same Type):
Spreads - Bull Spread (1) • Bull Spread: Buy 1 call option & sell 1 call option with higher strike price. Maturity is the same. Underlying asset is the same. Strike prices: X1 < X2. Assumption: E0(ST) .
Short put
Profit
X
ST
Long put
X
ST
Short stock
Protective put
Payoff from put
ST > X 0
Payoff Total from stock payoff
ST ST
Total profit
ST - cost = ST - St - p X - cost = X - St - p
ST >X -(ST - X)
Payoff Total from stock payoff
ST X
Total profit
X - cost = X – St + c ST - cost = ST – St + c
ST <X
0
ST
ST
There is a “plus” because we are selling the option
ST < X
X - ST
ST
X
Trading Strategies Involving a Single Option and a Stock (3)
Put-Call Parity: • p + S = c + e-rTX ==> p + S = c + M where M = e-rTX, M is money.
Options: Trading Strategies
Three Famous Strategies
• Take a position in the option and in the underlying (these strategies replicate other options) • Take a position in 2 or more options of the same type (Spreads) • Take a position in a mixture of calls & puts (Combinations)
Profit
X1 X2
X3
ST
Trading Strategies Involving Two Options (Different Types): Straddle (1)
• Straddle: Buy 1 call and 1 put. Same strike price and maturity. If the price of the underlying asset does not move too much (from X) ==> loss. If the price moves ==> profits.
Trading Strategies Involving a Single Option and a Stock: Profit Functions (1)
• Writing a covered call: Long in the stock & short in the call. • Reverse of writing a covered call: Short in the stock & long call.
Trading Strategies Involving a Single Option and a Stock: Profit Functions (2)
• Protective put: Long stock & long put.
Long stock
• Reverse of protective put: Short in the stock & short put. Profit