Trading Implied Volatility: Extrinsiq Advanced Options Trading Guides, #4

Part I : Introduction to Implied Volatility

Volatility has come to be seen as an asset class in its own right. Portfolio managers increasingly consider ‘trading volatility’ either to protect their holdings or to try to enhance their fund’s yield. But what does it mean to ‘trade volatility’? Volatility is a term used to refer to the amount of movement in a market or in markets generally. However there is an important distinction to draw. By volatility, traders can mean either the volatility that has already occurred or they can mean the volatility that is expected to occur. The former is known as the realised or historic volatility. The latter is known either as the expected volatility or, for reasons explained in what follows, as the implied volatility. Traders are typically more interested in the forward-looking meaning of the volatility. In other words, they can find more to disagree about in the level of implied volatility. Historic volatility has, by definition, already occurred and so there is less to dispute. Although in fact there is no single, definitive method for calculating historic volatility, this matters little in practice; since it is in the past, disagreements about measurement can only be resolved by back-tested paper-traded strategies. Much more interesting therefore is implied volatility; the volatility that is expected to occur next.

In Part I we shall begin by explaining the term ‘implied volatility’. After basic definitions we will discuss some of the factors that affect implied volatility; what causes it to rise and fall? We shall then look at the basics of trading implied volatility before considering some of the instruments commonly used to gain exposure to implied volatility.

What is implied volatility?

Implied volatility, as a term, originates in the options market. The value of an options contract is affected by several determinants, such as the current price of the underlying relative to the option strike and the time remaining until expiration. Another factor of great importance is the expected volatility of the underlying instrument over the life of the option. For out-of-the-money options to be worth anything at all, they must have some chance of expiring in-the-money. This requires the underlying spot product to exhibit some price volatility; its price needs to be moving in order for the option to have a hope of becoming valuable. The more volatile the spot product, the more valuable the option will be, whether it is a call or a put option.

When the option trader tries to value an option theoretically, using a mathematical model, one of the inputs will therefore be the volatility of the underlying expected over the life of the option. Notice that this is a single number. To produce a single, theoretical valuation of the option, option pricing models take a single value for the expected volatility. In other words, the value of an option maps uniquely to a level of expected volatility in the underlying. This explains how ‘implied’ became the term used for the ‘expected’ volatility that was plugged into the option pricing models. Since an option value is uniquely identifiable with one level of expected volatility, the option value (in dollars and cents) inherently implies the expected level of volatility. To generate an option value, determining factors are plugged into the model. But if one works in reverse and starts with the option value and all the other determining factors except the value for expected volatility, it is a relatively simple matter to rearrange formulae and make the expected volatility level the subject.

For example, assume the spot is trading at $100, interest rates are zero, the time to expiry is 36 days and the expected volatility in the underlying is set at 25%. The Black Scholes option pricing model will generate a value for the $100 strike call option of approximately $3.15. Instead, we could ask what is the implied volatility being used to value a call option if its value is $3.15, it has a strike of $100, the spot is trading at $100 and interest rates are zero? The answer would be 25%. This is the implied volatility.

Implied volatility is, in almost all cases, presented as an annualised number. So in the above example, 25% is the expected volatility in the underlying product for the life of the option but expressed as as an annualised number. Notice that the call option has only 36 days of life remaining and yet traders do not plug into the model the expected volatility over the next 36 days per se. The model does adjust accordingly, so that the annualised number that is inputted is appropriately amended for the option’s life-span. The reason for dealing in annualised (i.e. normalised) implied volatility is that it makes comparison so much simpler. Comparison between options of different strikes, different expirations and even with different underlyings. This standardisation makes trading implied volatility easier.

Interpreting Implied Volatility numbers

Implied Volatility numbers have useful, intuitive interpretations. It is important to note that often belying these interpretations are theoretical assumptions about the probability distributions that might be thought to be generating spot prices. In other words, these interpretations are theoretically logical and valid, but only true in reality as far as the assumptions hold true. Let’s make this clearer with some examples.

Implied volatility as a predictor