OPTIONS
Family Ties
Put/Call Parity
by Alex Mendoza
Here's a look at the basic relationships between calls and puts with
identical strikes and expiration dates.
According to the most common option pricing
models, volatility is equal for calls and puts with the same strike and
expiration. This rule originates from the construction of the Black-Scholes
model. Quite simply, since a call and its corresponding put expire at the
same time, time value in one should be equal to time value in the other.
Given that all of the other components of the option prices are known and
equal, it follows that a relationship must exist between the value of a
call and that of its corresponding put. While the various option pricing
models use partial differential equations to obtain these values, there
is a simpler way to establish put/call relationships.
ESTABLISHING REALTIONSHIPS
I'll begin by examining the graphical relationship between puts and
calls. Take a look at the option chain in Microsoft (MSFT), focusing on
the April 2004 options (see Figure 1).
1. Assuming MSFT is currently trading at $27.54, suppose you
purchase an April 2004 $27.50 call for $1.35. Your maximum risk is limited
to $1.35, while your maximum reward is unlimited to the upside. The reward
is shown in Figure 2.
2. Suppose that in addition to your call, you sell 100 shares of MSFT
at $27.54. The upside reward of your call would be canceled by the upside
risk of your short stock. The downside potential reward of the short stock
would still be attainable, and your risk to the position would be limited.
A quick look at the diagram in Figure 3 confirms that by selling stock,
you have transformed your long call position into a long synthetic put
position.
At least graphically, you can now state that:
Call - Stock = Put
By applying some simple logic, you also find that:
Put + Stock = Call
3. Using the MSFT example again, and supposing that you purchased
the April 2004 $27.50 put for $1.20 and bought 100 shares of MSFT at $27.54,
your risk picture looks like the one in Figure 4, which is indeed the picture
of a call.
Thus, it's clear that you can move back and forth between
puts and calls by simply buying or selling stock. Market makers and institutional
traders routinely take advantage of these relationships in order to maximize
their expected gains on every trade.
Figure 1: OPTION CHAIN OF MICROSOFT CORP. (MSFT). This option
chain of April 2004 options will be our example.
...Continued in the June issue of Technical Analysis of STOCKS &
COMMODITIES
Excerpted from an article originally published in the June 2004 issue
of Technical Analysis of STOCKS & COMMODITIES magazine. All rights
reserved. © Copyright 2004, Technical Analysis, Inc.
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