# The Surface of Options Volatility

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Years before Times Square was swept clean and sanitized you were a regular staple as a “Three Card Monte” dealer.  While setting up your cardboard box – giving you the ability to set-up and disappear quickly – you spot a callow-looking tourist (i.e. the “mark”) to play.  You place three cards face down on the box,  present the sightseer the queen of hearts as the “target card” then you shuffle the cards quickly to confuse him about which card it is.  He is now given the opportunity to correctly identify the queen of hearts.  If he does, he gets his “stake” back, plus the amount again, otherwise he loses.

The traveler knows the odds of picking the queen of hearts is 33.333%.  That is so because he doesn’t know which of the three cards is the queen of hearts – he is making an estimate, it can either be the left, center, or right card and since it needs to be one of them (there are three possibilities yet one probability), he can immediately presume that the probability of choosing the correct card is 33.333%. His estimation is based on a shortage of information on his part yet, a shortage of information with identifiable possibilities.

Probability is nothing but a function of how much information we have; it’s the possibility of a particular event occurring.  However, mingling any probability concept, function, or measure with financial markets – where possibility combinations and ultimate outcomes are basically limitless – lies somewhere between an esoteric art form and plain foolery.

The Volatility Surface

An options implied volatility is the greatest expression of a financial system together attempting to harness, estimate, or place odds on an asset’s pathway within the context of a pre-defined time parameter.  And yet, what grows so peculiar is the vast spectrum of option risk management and valuation tools including – the bell curve and value-at-risk (V@R) are, within their knitting, intimately predicated on the assumption or, the concept of probability.

The widespread, day-to-day practice of valuing option prices in terms of some esoteric model in no way implies the options industry believes underlying returns to be part of a bell curve or, normal distribution.  Quite the contrary, as the variations of implied volatility across option strikes and months, which is referred to as the volatility surface, can be sizeable.  We refer to an options implied volatility across option strikes as skew and volatility across months as term-structure and together they form the volatility surface.

Implied Volatility Skew

Since 1987’s “Black Monday” stock market crash, equity and equity index “volatility surfaces” have been described by its implied volatility skew.  That is, for a given expiration date, implied volatilities tend to increase as strike price decreases for strikes below the current underlying price.  Oppositely, options implied volatilities tend to decrease as strike price increases for strikes above the current underlying price.  This tendency should be rather logical because options consensus, aware that equity markets crash downwards more than they melt-up, would price out-of-the money puts with higher implied volatility compared to at-the-money puts.

Another way of grasping skew is since we reside in a net long equity world, there is a bias for equity investors to protect their holdings by purchasing downside puts (protection) while selling upside calls for income enhancement.  This is a simple supply versus demand issue – placing a natural over demand for out-of-the-money put buyers coupled with a simultaneous over-supply of out-of-the-money call sellers.

On the other hand, various commodities (e.g. corn, coffee, soybeans) may display the exact opposite options skew (i.e. options implied volatility for out-of-the-money calls is higher than equidistant out-of-the-money puts) as the outlier shock to these commodities would be to the upside NOT the downside.

Other words, agricultural markets have “shocks” to the upside (e.g. 2013) – higher prices may be good for the farmer but disastrous to everyone else thus, consensus is a natural buyer of out-of-the-money calls (protection) while selling downside puts for income enhancement.

Implied Volatility Term Structure

The next step in viewing the volatility surface is to identify the assets implied volatility term structure or, the options implied volatilities (per strike price) across different expiration dates.  The relationship of an equity option’s at-the-money implied volatility for a 30-day option compared to a 60 or 90-day option, like options skew, is fluid and subject to variation due to changes in market confidence, supply vs. demand and, these fluctuations are described by participants as term-structure that is steep, flat, or inverted.

“Steepness” (i.e. deferred month volatility is extraordinarily higher than near-term volatility) in the term would suggest that consensus perceives much less volatility in the short-term as compared to the long-term. A “flat term” (i.e. volatility between months is relatively flat compared to history) suggests there is no – or much less - extra implied volatility associated with time.

A downward sloping or “inverted term” (i.e. short-term volatilities are relatively higher than longer dated volatilities) is the result of a current bleak circumstance, one that consensus view as being temporary which is reflected in lower volatilities the further one goes out in time.

Importance of the Volatility Surface

Given it’s a group portrait of all strike prices and expiration dates, the volatility surface winds up presenting itself as a three-dimensional plot; one that can be helpful in allowing you to perceive the larger picture of an assets implied volatility.  Its culmination effect may help in distinguishing the forest from the trees – allowing the trader to make higher expectancy risk-reward trades or risk management decisions.  It could help certain your uncertainty.