Option Combinations and Positions

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 priceP = put price F = forward priceK = strike price Same 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

Q: Put-Call Parity (From Exam FM Fin Econ Sample Questions)

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(K 1 ), short C(K 2 ) (K 1 < K 2 ) –Bear: short C(K 1 ), long C(K 2 ) (K 1 < K 2 ) –Box: combination of bull and bear spreads –Ratio: unequal numbers of the different options Collar: –Long P(K 1 ), short C(K 2 ) (K 1 < K 2 )

Option Combinations (cont.) Straddle –Long P(K 1 ), long C(K 1 ) Written straddle –Short P(K 1 ), short C(K 1 ) 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., + = K1K1 K2K2 K1K1 K2K2

Q: Relationship Between Derivative and Underlying Asset (From Exam FM Fin Econ Sample Questions)

Q: Option Positions – Spreads (From Exam FM Fin Econ Sample Questions)

Q: Option Positions – Spreads (cont.) (From Exam FM Fin Econ Sample Questions)

Q: Option Positions - Straddles (From Exam FM Fin Econ Sample Questions)

Q: Option Positions – Collars (From Exam FM Fin Econ Sample Questions)