# What is implied volatility?

When valuing options, a number of factors have to be taken into account. Most of these are known and there is no room for argument about their value. For example, the strike of the option relative to the price of the underlying product, has an impact on the option’s value. Calls whose strike is below the underlying product price are worth more than calls whose strike is above the underlying product price. But the point is that there is no disagreement about either the strike of the option or the price of the underlying. The same is true for the expiration date of the options; this is known by everybody and is not a matter of contention.

However, there is one crucial element in the valuation of options which is not known in advance with certainty. This is the volatility level in the price of the underlying product that will be realized during the option’s lifespan. Let’s think about this more carefully. Suppose you are offered the option to take an umbrella out when you go for a long walk. What is this option worth? To answer that, you really need to know how *likely it is to rain. *With financial options, the same idea applies. If you knew with absolute certainty whether rain was going to fall, you could value the option accurately. But if you can’t be sure about the likelihood of rain, then this introduces *uncertainty* into your valuation. With financial options, the same reasoning works. It is very unlikely that you know for certain where the price of the underlying product will be trading when the options expire. Instead, you can still value the option by estimating *how volatile* the price of the underlying product will be.

So, a number of factors go into valuing an option. Most of these are known with certainty and are not debatable. But a very important element of the option valuation is the expected volatility level of the underlying product price. Now we come to *implied volatility.* If you know the price of an option, perhaps because you can see where it is trading in a market, then you can work out the level of volatility that is being used to value the options: in other words the volatility level in the underlying that is *implied* by the price of the option.

Another way to see this is if you think of a rectangle whose width is known to everybody, but whose height is unknown. If there was a market trading in the *area* of the rectangle, then by a simple re-arrangement of the equation for the area of a rectangle, you could work out the *implied* height of the rectangle which is implied by the market in the area. Similarly with options; if you know their price, you can work out the volatility level being used by traders in the calculation to arrive at the value. And this is what is known as implied volatility.

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