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# Are Calls and Puts Equal?

Many times the issue comes up as to whether calls and puts are truly equal. Rather than simply giving the answer, several points will be presented in order to lead the reader to draw their own conclusion.

First, let us look at the option chain, Figure 1, and observe a simple issue. If we look at the options that are out-of-the-money, for instance two steps, and assume that indeed the calls are as equally priced as the puts, what do we see?

Figure 1: Home Depot on 1/31/2012

The underlying selected (HD = Home Depot) was chosen because of its nearness to the 50 cents mark. When the snapshot was taken, it was trading very close to 44.50, hence, a two step OTM call would be the 46 call strike price. 46 is approximately 1.50 away from the current stock price. By the same token, a two step OTM put would be the 43 strike. Again, the 43 strike put is 1.50 away from the current price. Therefore, having found nearly equal distant OTM puts and OTM calls, we can ask, ‘Are they equally priced in terms of their premium?’ The answer is in Figure 1 and not in the text.

Is there more risk to the market makers from the downside or upside potential? Market makers do have the ability to stretch extrinsic premium, but not intrinsic.

Having made the first point, we can move on to the Greek components that we should be focusing on when evaluating options; namely Delta, Vega, and Theta. If we focus on long options (long call = + C, and long put = + P), then we should be aware of the fact that some of the Greeks are going to be helping our premium while others will be detrimental to it. At this point, we can no longer make any general statements about long options because we have come to a fork in our road. Hence, let us separately look at an example of a long call (+ c) first and then + p.

### PART I: + C

If we want to select a call on HD that is deep in-the-money with a delta near 80 cents, then the logical choice would be the 42 strike price call. It already has intrinsic value of nearly 2.50. The Bid and Ask prices are 2.70 and 2.74 with the mid price being 2.72. If HD goes from its current price up one handle, then our 42 call would be (2.74 + 0.82) 3.56 which is shown on the next figure.

Figure 2

Notice that in the Layout, we have asked the platform to display Theoretical Price, Mark (mid of B/A) and Delta. In order to verify if our new premium of the long Feb 42 call is really going to be 3.56, our focus should be on the Theo Price. After we typed in the box Stock Price Adjusted plus one (+1.00), standing for the underlying moving up one handle, the Bid, Ask, Delta, and Mark did NOT change their values at all. But Theo Price changes because we have altered it by +1.00. Notice that the date (1/31/2012) did not get tweaked, therefore, the assumption is that within the same trading session, the market has moved up a point. However, this is not reality. A single Greek component (Delta) does not move in isolation from the others; time (Theta) passes by and volatility (Vega) is dynamic. Hence, if we could properly manipulate these other two components (Theta and Vega), we would have infinite possibilities for the Theoretical Price. Out of all the possibilities, what we truly want as a buyer of a long call is presented in Figure 3 below.

Greeks

+ c = a long call

Our goal is to see

Underlying goes up

 Delta + Helps/Benefits Delta gain value Increases Vega + Helps/Benefits Vega increase Decreases Theta – Hurts Theta to stand still Decreases
Figure 3: If the underlying goes up

When the underlying goes up, out of the three Greeks on the long call, only one is truly working in the favor of the buyer of that long call. Now, let us see if the case is the same with a long put.

### PART II: + P

Taking the same Greeks into consideration, we should notice that if the underlying goes down, we might have more things working for us rather than against us. For example, besides our Delta increasing the value of the premium when HD drops, our Vega might increase due to fear caused by a drop in HD’s value. In that case, the increases in Vega and Delta might easily overcome Theta decay.

Greeks

+ p = a long put

Our goal is to see

Underlying goes down

 Delta + Helps/Benefits Delta gain value Increases Vega + Helps/Benefits Vega increase Increases Theta – Hurts Theta to stand still Decreases
Figure 4

In conclusion, this article has addressed the issue of the long call versus the long put. Rather than simply giving the answer – NO they are NOT equal – several points were presented in order to lead the reader to the conclusion. Markets tend to go down faster due to the g-force (gravity) and market makers know how to protect themselves so they price put options at a different level from their call counterparts. Know your options before you trade them.

– Josip Causic

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