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 = PutBy applying some simple logic, you also find that:
Put + Stock = Call3. 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.
...Continued in the June issue of Technical Analysis of STOCKS & COMMODITIES
Figure 1: OPTION CHAIN OF MICROSOFT CORP. (MSFT). This option chain of April 2004 options will be our example.
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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