f b e559f15 trading strategies
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Trading Strategies
Portfolios of Options
Introduction
• Put-call parity: replication of positions in the underlying.
• Allow for very flexible types of payoffs (portfolios of options).
• Risk management:– Hedging risks.– Portfolio insurance: Stock + Put.
Relationship with Underlying
• Remember the put-call parity:
P + S = C + PV(X)
• PV (X) is independent of underlying.
• Long Stock + Long Put ~ Call.
• Short Stock + Short Put ~ Short Call.
• Short Stock + Long Call ~ Long Put.
• Long Stock + Short Call ~ Short Put.
Example
S
Payoff
0
Long Stock+ Long Put ~ Long Call
Long Put
Long StockLong Call
Spreads
• They involve investing in options of the same type, but with different strike price.
• Bull spread (1):– Buy call with low X.– Write call with high X.
• Bull spread (2):– Buy put with low X.– Write put with high X.
Bull Spread (1)
S
Payoff
0
Long Call (X1) + Short Call (X2)
Long Call
X2
X1
Bull Spread (2)
S
Payoff
0
Long Put (X1) + Short Put (X2)
X2
X1
Bull Spread with Calls (Example)
• Prices of securities:– S = 47.
– C(X=45) = 3.
– C(X=50) = 0.54.
• Buy a call with strike price 45 and write a call with strike price 50. Cost: 3-0.54 = 2.46.
• When S is lower than 45, both calls are out of the money and we lose the investment in the portfolio.
• When S is above 45, but below 50, only the call we bought is in the money. Net payoff:
S - 45 - 2.46 = S - 47.46
Bull Spread (Example, cont.)
• When the stock price is above 50, both options are in the money. The net payoff is,
S – 45 – (S – 50) – 2.46 = 2.54• In summary,
Net Payoff S < 45 -2.46
45 < S < 50 S - 47.46 50 < S 2.54
• And the break-even point is S = 47.46
Spreads (cont.)
• Bear spread (1):– Buy call with high X.– Write call with low X.
• Bear spread (2):– Buy put with high X.– Write put with low X.
Bear Spread (1)
S
Payoff
0
Short Call (X1) + Long Call (X2)
Long CallX2X1
Bear Spread (2)
S
Payoff
0
Short Put (X1) + Long Put (X2)
X2
X1
Butterfly Spreads
• Positions in options with three different strike prices.
• Butterfly spread with calls:– Buy one call with low X and one with high X.– Write two calls with a X halfway in between.
• Butterfly spread with puts:– Buy one put with low X and one with high X.– Write two puts with a X halfway in between.
Calendar Spreads
• Positions in options with same strike price and different maturities.
• Options with longer maturities are more expensive.
• Bullish or bearish, depending on the relationship of the strike price to the price of the stock today.
Butterfly Spread (1)
S
Payoff
0
Long Call (X1) + 2 Short Calls (X2) + Long Call (X3)
X2
X1 X3
Butterfly Spread (2)
Long Put (X1) + 2 Short Puts (X2) + Long Put (X3)
S
Payoff
0
X2
X1 X3
Calendar Spread (1)
S
Payoff
0
Short Call (T1) + Long Call (T2)
X
Calendar Spread (2)
S
Payoff
0
Short Put (T1) + Long Put (T2)
X
Combinations
• Position in both calls and puts.
• Straddle: buy a put and a call with same strike price.
• Strangle: buy a put and a call with different strike prices.
• Strip: buy one call and two puts with same strike price.
• Strap: buy one put and two calls with same strike price.
Straddle
S
Payoff
0
Long Put (X) + Long Call (X)
X
Strangle
S
Payoff
0
Long Put (X1) + Long Call (X2)
X1 X2
Strip
S
Payoff
0
2 Long Puts (X) + Long Call (X)
X
Strap
S
Payoff
0
Long Put (X) + 2 Long Calls (X)
X
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