winter2010_notes_part3

winter2010_notes_part3 - IBM Option Quotes 1-1 Put-Call...

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1-1 IBM Option Quotes
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1-2 Put-Call Parity For European options with the same strike price and time to expiration the parity relationship is Call – put = PV (forward price – strike price) or Intuition Buying a call and selling a put with the strike equal to the forward price ( F 0 ,T = K ) creates a synthetic forward contract and hence must have a zero price C ( K , T ) P ( K , T ) = PV 0, T ( F T K ) = e rT ( F T K )
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1-3 Parity for Options on Stocks If underlying asset is a stock and Div is the dividend stream, then e -rT F 0 ,T = S 0 PV 0, T ( Div ), therefore Rewriting above For index options, , therefore C ( K , T ) = P ( K , T ) + [ S 0 PV 0, T ( Div )] e rT ( K ) S 0 = C ( K , T ) P ( K , T ) + PV T ( ) + e rT ( K ) C ( K , T ) = P ( K , T ) + S 0 e δ T PV T ( K ) S 0 PV T ( ) = S 0 e T
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1-4 Parity for Options on Stocks (cont’d) Examples 9.1 & 9.2 Price of a non-dividend paying stock: $40, r=8%, option strike price: $40, time to expiration: 3 months, European call: $2.78, European put: $1.99. $2.78=$1.99+$40 $40 e -0.08x0.25 Additionally, if the stock pays $5 just before expiration, call: $0.74, and put: $4.85. $0.74=$4.85+($40 $5 e -0.08x0.25 ) $40 e -0.08x0.25 Synthetic security creation using parity Synthetic stock: buy call, sell put, lend PV of strike and dividends Synthetic T-bill: buy stock, sell call, buy put (conversion) Synthetic call: buy stock, buy put, borrow PV of strike and dividends Synthetic put: sell stock, buy call, lend PV of strike and dividends
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1-5 Generalized Parity Relationship C ( S T , Q T , T t ) P ( S T , Q T , T t ) = F P t , T ( S ) F P t , T ( Q )
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1-6 Properties of Option Prices American versus European Since an American option can be exercised at anytime, whereas a European option can only be exercised at expiration, an American option must always be at least as valuable as an otherwise identical European option C Amer ( S , K , T ) > C Eur ( S , K , T ) P Amer ( S , K , T ) > P Eur ( S , K , T )
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1-7 Properties of Option Prices (cont’d) Option price boundaries Call price cannot be negative exceed stock price be less than price implied by put-call parity using zero for put price: Put price cannot be more than the strike price be less than price implied by put-call parity using zero for call price: S > C Amer ( S , K , T ) C Eur ( S , K , T ) max[0, PV 0, T ( F T ) PV T ( K )] K > P Amer ( S , K , T ) P Eur ( S , K , T ) max[0, PV T ( K ) PV T ( F T
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1-8 Properties of Option Prices (cont’d) Early exercise of American options A non-dividend paying American call option should not be exercised early, because That means, one would lose money be exercising early instead of selling the option If there are dividends, it may be optimal to exercise early It may be optimal to exercise a non-dividend paying put option early if the underlying stock price is sufficiently low C Amer C Eur S T K
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1-9 Properties of Option Prices (cont’d) Time to expiration An American option (both put and call) with more time to expiration is at least as valuable as an American option with less time to expiration. This is because the longer
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This note was uploaded on 04/13/2010 for the course FIN 823 taught by Professor Keweiho during the Spring '10 term at Ohio State.

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winter2010_notes_part3 - IBM Option Quotes 1-1 Put-Call...

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