PCP (no, not PCP) is a fundamental relationship that must exist between the prices of put (P) and call (C) options with the same underlying stock (U). The relationship is derived from a simple arbitrage argument: if they were not the same, then an arbitrage opportunity would exist (more on this later).
The simple relationship is:
C+PV(K)=P+U
C
- Current price of a call option
- PV(
K)
- Risk-free instrument (i.e. cash in the bank) with a value equal to the present value of the strike price (
K)
P
- Current price of a put option
U
- Current value of underlying share
The call option is only exercised if the underlier's final value is greater than the strike price: the risk-free investment eliminates the downside. Similarly the put option is insulated by actually having the share-- it is only exercised if the underlier's value is below the strike price.
Options are traded on just about anything-- i.e. debt can be viewed as an option to repurchase an asset from a creditor, etc. The price of the option is subtracted from any economic profits earned by buyer or seller, and the value of both portfolios must be the same because of their identical outcomes. If this were not true, one would purchase the less expensive and sell the other, earning arbitrage profits. As we all know, down that road lies pain, anger, madness, and market inefficiency.
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