Put Call Parity - Definition
Put Call Parity is an option pricing concept that requires
the extrinsic values of call and put options to be in equilibrium so as to prevent
arbitrage. Put Call Parity is also known as the Law Of One Price.
Put Call Parity - Introduction
Put Call Parity requires, mathematically, that option trading positions with similar payoff or risk profiles (i.e Synthetic Positions)
must end up with the same profit or loss upon expiration such that no arbitrage opportunities exist.
An example of Put Call Parity is in terms of Fiduciary Calls
and Protective Puts. Fiduciary Calls and Protective Puts have the same
profit/loss profile that you see below.
If the underlying stock remains completely stagnant by expiration of both positions, both positions would decline in value equal to
the extrinsic value (premium) paid on the options. Neither option trading positions would have any advantage over the other during expiration.
Put Call Parity Theorem - Calculating Put Call Parity
The mathematical representation of Put Call Parity in the case of Fiduciary Calls and Protective Puts is:
C + X / (1+RFR)t = S + P
Where : c = Call premium, X / (1+RFR)t = Present value of strike price, S = initial stock price, P = Put premium
Each of the securities in the Put Call Parity Theorem can thus be expressed as:
Stock Price = C - P + X / (1+RFR)t
Put Premium = C - S + X / (1+RFR)t
Call Premium = S + P - X / (1+RFR)t
Present Value Of Strike Price = S + P - C
The above relationships assumes that no dividends are being paid. The Put Call Parity Theorem for dividend paying stocks is:
P = C - S + x/(1+RFR)t + d/(1+RFR)t
C = P + S - x/(1+RFR)t - d/(1+RFR)t
Where d = Dividend To Be Paid
Put Call Parity - Limitations
Put Call Parity applies mainly to European style options as American Style options allows early exercise which can result in
profit opportunities that lies beyond the Put Call Parity Theorem.
Put Call Parity - Assumptions
The assumptions under the Put Call Parity Theorem are:
1. Constant Interest Rate
2. Future dividends are known for sure
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