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Equity and Index Options Explained by W. A. Beagles

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8

Skew

Skew is a real world phenomenon, a feature routinely observed in the majority of option markets.

What does “skew” mean in a wider context? Skew is asymmetry, imbalance. To describe something as “skewed” is to describe it as twisted, distorted, out of shape. How might this apply to options and to option markets? Let's consider how option prices should look in a perfectly mathematical, emotionless world.

Consider the set of option prices in Table 8.1. At this stage, they are just numbers. Consider them as such; don't think about the underlying, just think about the numbers.

First, consider the at-the-money options; the 200 strike. Both the 200 calls and the 200 puts are worth 10. Why? Why should at-the-money calls and puts always be the same price? Because they have an equal chance of “success”. They have an equal chance of being in-the-money upon expiry. Given that the underlying is trading at exactly 200, the 200 call has a 50% chance of being in-the-money on expiry because there is a 50% chance of the underlying going up and a 50% chance of it going down. Likewise, the 200 put has a 50% chance of being in-the-money on expiry because there is a 50% chance of the underlying going down and a 50% chance of it going up.

These equal chances of “success” manifest themselves in equal prices. Given that the underlying is at exactly 200 and that the options are exactly at-the-money, the above is mathematical fact.

Table 8.1 ZYX 3 month option prices (3 month ZYX future = 200)

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