Insuring Long Asset: Protective Put
• Investor owns asset• Investor also buys (holds) a put on the asset• Guarantees investment portfolio proceeds are at
least equal to the exercise price of the put• Similar to net position of asset+insurance• Protective put = long asset + long put = long call
+ lending (shape same as long call, but up)
+ =
Insuring Short Asset
• Investor shorts asset• Investor also buys (holds) a call on the asset• Limits downside of short asset position• Short asset + long call = long put + borrowing
(shape same as long put, but shifted down)
+ =
Selling Insurance: Covered Call
• Investor purchases asset• Investor also sells (writes) a call option on the
asset• Option position is “covered” by owning the
underlying asset itself• Similar to shifted written put• Provides additional (premium) income
+ =
Other Option Positions
• Naked call– Short call option– No position in underlying asset– Potentially unlimited loss
• Covered put– Short put + short asset– Shape: short call, but shifted down
Put-Call Parity
• General formula:
C – P = PV(F) – PV(K)where: C = call price P = put price
F = forward price K = strike priceSame K, T, and U/L asset for call, put
• For non-dividend-paying U/L asset:
C – P = S – PV(K)
where: S = current price of U/L asset
Option Combinations
• Synthetic forward– Long call plus short put (same exercise price K)– Guarantees buying asset at K
• Spread (also see subsequent slide)– Bull: long C(K1), short C(K2) (K1 < K2)– Bear: short C(K1), long C(K2) (K1 < K2)– Box: combination of bull and bear spreads– Ratio: unequal numbers of the different options
• Collar:– Long P(K1), short C(K2) (K1 < K2)
Option Combinations (cont.)
• Straddle– Long P(K1), long C(K1)
• Written straddle– Short P(K1), short C(K1)
• Strangle– Like straddle, but use less expensive out-of-the-
money options
• Butterfly spread– Written straddle + long Cs and Ps (out-of-the-money)– Asymmetric: unequal numbers of options
Generally use at-the-money options
Spread
• Combination of options– Two or more calls, or– Two or more puts
• Horizontal spread: sale and purchase of options with different expiration dates
• Vertical spread: simultaneous sale and purchase of options with different exercise prices -- e.g.,
+ =K1
K2
K1 K2
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