Effect of increasing a factor on the price of an option:
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 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
Fiduciary call Protective put
Put call parity only holds for European option. For American options, we have an inequality.
S0 – X ≤ C – P ≤ S0 – Xe – r T
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.
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
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