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**Put-Call Parity**

Put-call parity holds that portfolio with identical payoffs must sell for the same price to prevent arbitrage, the put-call parity relationship.

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c + X/(1+RFR)^{T} = S+p

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If the asset has an underlying stream of cash flows, the put-call parity can change to:

c_{0}+(X/(1+r)^{T}) = p_{0} + [S_{0}PV(CF,0,T)]

- Buyer of a call option - long position in Call
- Writer of a call option - short position in Call
- Buyer of a put option - long position in Put

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Writer of a put option - short position in Put

Intrinsic value of a call option = Max [O, S - X]

Intrinsic value of a put option = Max [O, X - S]

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Example

The stock of a company is trading at $108.

1 year European call options with a strike price of $100 has a premium of $5 Interest rate is 8%. Find the premium of a 1 year European put option with a strike of $100.

Solution

$5

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