Put-Call Parity
Put and call values are mathematically bound together by an equation
referred to as put-call parity. In its basic form, put-call parity states:
where
c = call value,
PV(x) = present value of the strike price,
p = put value, and
s = stock price.
The put-call parity assumes that options are not exercised before
expiration (that is, that they are European style). This version of the put-call
parity is for European options on non-dividend-paying stocks. Put-call
parity can be modified to reflect the values of options on stocks that pay
dividends. In practice, equity-option traders look at the equation in a
slightly different way:
Traders serious about learning to trade options must know put-call parity
backward and forward. Why? First, by algebraically rearranging this
equation, it can be inferred that synthetically equivalent positions can be
established by simply adding stock to an option. Again, a put is a call; a call
is a put.
and
For example, a long call is synthetically equal to a long stock position
plus a long put on the same strike, once interest and dividends are figured
in. A synthetic long stock position is created by buying a call and selling a
put of the same month and strike. Understanding synthetic relationships is
intrinsic to understanding options. A more comprehensive discussion of
synthetic relationships and tactical considerations for creating synthetic
positions is offered in Chapter 6.