C13 PROPERTIES OF STOCK OPTIONS

FACTORS EFFECTING OPTION PRICES #

Effect of increasing a factor on the price of an option:

LOWER & UPPER BOUNDS FOR OPTIONS #

Where,  c = value of European call option

C = value of American call option

p = value of European put option

P = value of American put option

PUT CALL PARITY #

Put call parity is the relationship that must exists between the prices  of European put & call option, having same underlie, strike price and expiration date.

 Call + Xe ^{– rT} = S₀  + Put  

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Fiduciary call      Protective put 

RELATIONSHIP BETWEEN AMERICAN CALL & PUT OPTION #

Put call parity only holds for European option. For American options, we have an inequality.

S₀  – X ≤ C – P ≤ S₀ – Xe ^{– r T}

IMPACT OF DIVIDENDS ON OPTION PRICING BOUNDS #

To prevent arbitrage, when a stock pays a dividend, its value must decrease by the amount of the dividend. This increases the value put & decreases the value of call.

European option:

c ≥ S₀ – D – Xe ^{– r T}

p ≥ S₀ – D – Xe ^{– r T}

Early exercise of American option:

P + S₀  = C + D + Xe ^{– r T}

S₀ – X –D ≤ C – P ≤ S₀  – Xe ^{– r T}