|
Put-call parity
is a relationship, first identified by Stoll (1969), that must exist between the
prices of European put and call options that both have
the same underlier,
strike price and expiration date.
The relationship is derived using arbitrage
arguments. Consider two portfolios consisting of:
 The call option and an amount
of cash equal to the present value of the strike price.
The put option and the
underlier.
Exhibit 1 compares the
expiration value for these two portfolios, with x representing the common
strike price:
|
|
 |
 |
|
A portfolio comprising a call option and
an amount x of cash equal to the present value of the option's strike
price has the same expiration value as a portfolio comprising the
corresponding put option and the underlier. For European options,
early exercise is not possible. If the expiration values of the two
portfolios are the same, then their present values must also be the
same. This equivalence is put-call parity. |
What is significant about
Exhibit 1 is the fact that the two portfolios (call + cash and put + underlier)
have identical expiration values. Irrespective of the value of the underlier at
expiration, each portfolio will have the same value as the other.
If the two portfolios are going
to have the same value at expiration, then they must have the same value today.
Otherwise, an investor could make an arbitrage profit by purchasing the less
expensive portfolio, selling the more expensive one and holding the long-short
position to expiration. Accordingly, we have the price equality:
where:
c = the current
market
value of the call;
PV(x) = the
present value of the strike price x, discounted from the expiration date
at a suitable risk free rate;
p = the current market
value of the put;
s = the current market
value of the underlier.
Equation [1]
is the put-call parity. Note that it is not based on any
option pricing model. It was derived
purely using arbitrage arguments. It applies only to European options, since a possibility of early exercise could
cause a divergence in the present values of the two portfolios.
Put-call parity offers a simple test of
option pricing models. Any option pricing model that produces
put and call prices that do not satisfy put-call parity must be
rejected as unsound. Such a model will suggest trading
opportunities where none exist.
|
|
|
|
|
 arbitrage-free pricing
The approach to pricing instruments that underlies essentially all of financial
engineering.
delta
hedge A type of hedge that is widely used by derivative
dealers to reduce or eliminate a portfolio's exposure to some
underlier.
interest
rate parity An arbitrage condition that must hold between the spot interest
rates of different currencies.
option
A type of derivative instrument.
option
spreads Positions combining one or more options in a single
underlier.
time value and
intrinsic value
The two components that comprise an option's market value.
option pricing theory The
body of financial theory used by financial engineers to value options and other
derivative instruments. |
|
|
|
|
|
 |
Ads by Contingency Analysis
|
|
|
|
|
|
Haug (1997)
is a handy encyclopedia of options pricing formulas. It includes a
discussion of put-call parity. For options trading, start with Natenberg (1994)
or Ward (2004)
before proceeding to Baird (1993). Cox and Rubinstein (1985)
is a classic. Pretty much everyone who works with options has read
it at some point.
|
|
|
|
|
|
 |
|
|
|
|
|
|
 Stoll, Hans R. (1969). The
relationship between put and call option prices, Journal of
Finance, 23, 801-824. |
|
Disclaimer
website:
http://www.contingencyanalysis.com
glossary direct link:
http://www.riskglossary.com
copyright © Contingency Analysis, 1996 -
current
|
_125.gif)
_125.gif)
_125.gif)
_125.gif)
_125.gif)
