Lecture 2: Option Strategies

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Lecture 2 Option Strategies

• Long vs. short positions
• Options in portfolios
• synthetic calls and puts
• collar
• riskless hedge
• spreads, straddles strangles
• butterflies

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Long vs. short positions

• Long position has a profit/loss diagram identical
  to that of a Forward contract
• Short position resembles a Forward sale

?
Pstock price
3

• With a long position, we buy the asset (or rights
  to it) now, in order to sell it later
• Long call (EX50 P50 Call6)
• Naked call

? max(P-EX,0)-call
?
? call - max(P-EX,0)
6
P
50
4

• Long put (EX50 P50 Put4.5)
• Short (written) put

?
? max(EX-P,0)-put
50
P
-4
?
? put - max(EX-P,0)
4
P
50
5
Protective Put

• a.k.a. insurance or synthetic call
• Buy stock (P50)
• Buy put (EX50, Put4)

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Collar

• Buy stock (P50)
• Buy put (EX50, Put4)
• Write call (EX55, Call2)

P
7
Riskless hedge

• In collar, ceiling - floor difference in EX
• When EXs are equal, we have perfect hedge,
  riskless profit
• On April 2
• Microsoft stock P 57.30
• July call (EX 60) Call 2.90
• July put (EX 60) Put 5.30

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Riskless hedge

• Net investment outlay 57.30 5.30 - 2.90
  59.70
• Rate of return 0.30 / 59.70 0.005025
• 0.005025 x 365 / 108 0.01698
• July Treasury yield 1.78
• We have a synthetic T-bill

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Covered Call

• Short call stock
• synthetic put

?
6
50
P
10

• So,
• protective put resembles a call
• covered call resembles a put
• collar resembles ?

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Bull spread Bear spread

• Long call (EX50, Call6)
• Short call (EX55, Call2)
• Bull spread
• compare to stock put - call collar

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Bull spread Bear spread

• Short call (EX50, Call6)
• Long call (EX55, Call2)
• Bear spread ( st. stock st. put long call)

?
50
-1
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Straddles

• Long call (EX50, Call6)
• Long put (EX50, Put4)
• opposite of naked straddle

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Strangles

• Long call (EX55, Call2.50)
• Long put (EX45, Put1.50)
• opposite of short strangle

?
50
long strangle
-4
15
Butterflies

• Short call (EX45, Call11)
• Short call (EX55, Call2.50)
• 2 long calls (EX50, Call6/ea.)

?
-1.5
-3.5
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Portfolio insurance

• Equity portfolio highly correlated w/ e.g. SP100
  (OEX)
• Apr 2, 2002 OEX 575 points
• Portfolio value 460,000
• Jun OEX put EX 570 x 100 57,000 Put
  18.50 x 100 1,850.00
• of contracts needed 460,000 / 57,500 8

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?
575
P
-18,800
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