Fx options volatility skew

Volatility Skew.

What is the 'Volatility Skew'

The volatility skew is the difference in implied volatility (IV) between out-of-the-money options, at-the-money options and in-the-money options. Volatility skew, which is affected by sentiment and the supply and demand relationship, provides information on whether fund managers prefer to write calls or puts. It is also known as a "vertical skew."

BREAKING DOWN 'Volatility Skew'

A situation where at-the-money options have lower implied volatility than out-of-the-money options is sometimes referred to as a volatility "smile" due to the shape it creates on a chart. In markets such as the equity markets, a skew occurs because money managers usually prefer to write calls over puts.

The volatility skew is represented graphically to demonstrate the IV of a particular set of options. Generally, the options used share the same expiration date and strike price, though at times only share the same strike price and not the same date. The graph is referred to as a volatility “smile” when the curve is more balanced or a volatility “smirk” if the curve is weighted to one side.

Volatility.

Volatility represents a level of risk present within a particular investment. It relates directly to the underlying asset associated with the option and is derived from the options price. The IV cannot be directly analyzed. Instead, it functions as part of a formula used to predict the future direction of a particular underlying asset. As the IV goes up, the price of the associated asset goes down.

Strike Price.

The strike price is the price specified within an option contract where the option may be exercised. When the contract is exercised, the call option buyer may buy the underlying asset or the put option buyer may sell the underlying asset.

Profits are derived depending on the difference between the strike price and the spot price. In the case of the call, it is determined by the amount in which the spot price exceeds the strike price. With the put, the opposite applies.

Reverse Skews and Forward Skews.

Reverse skews occur when the IV is higher on lower options strikes. It is most commonly in use on index options or other longer-term options. This model seems to occur at times when investors have market concerns and buy puts to compensate for the perceived risks. Forward skew IV values go up at higher points in correlation with the strike price. This is best represented within the commodities market where a lack of supply can drive prices up. Examples of commodities often associated with forward skews include oil and agricultural items.

Volatility Smile.

What is a 'Volatility Smile'

A volatility smile is a common graph shape that results from plotting the strike price and implied volatility of a group of options with the same expiration date. The volatility smile is so named because it looks like a person smiling. The implied volatility is derived from the Black-Scholes model, and the volatility adjusts according to the option's maturity and the extent to which it is in-the-money (moneyness).

BREAKING DOWN 'Volatility Smile'

The Volatility Smile Enigma.

The volatility smile is peculiar because it is not predicted by the Black-Scholes model, which is used to price options and other derivatives. The Black-Scholes model predicts that the implied volatility curve is flat when plotted against the strike price. It would be expected that the implied volatility would be the same for all options expiring on the same date regardless of strike price.

Explanations for Volatility Smile.

There are several explanations for the volatility smile. The volatility smile may be explained by investor demand for options of the same expiration date but disparate strike prices. In-the-money and out-of-the-money options are usually more desired by investors than at-the-money options. As the price of an option increases all else equal, the implied volatility of the underlying asset increases. Because increased demand bids the prices of such options up, the implied volatility for those options seem to be higher. Another explanation for the enigmatic strike price-implied volatility paradigm is that options with strike prices increasingly farther from the spot price of the underlying asset account for extreme market moves or black swan events. Such events are characterized by extreme volatility and increase the price of an option.

Implications for Investing.

The volatility smile is used in the analysis of a number of investments. It cannot be directly observed in over-the-counter foreign exchange markets, though investors can use at-the-money volatility and risk data for specific currency pairs to create a volatility smile for a specific strike price. Equity derivatives show price and volatility pairs, allowing the smile to be created relatively easily.

The volatility smile was first seen after the 1987 stock market crash, and it was not present before. This may be the result in changes in investor behavior, such as a fear of another crash or black swan, as well as structural issues that go against Black-Scholes option pricing assumptions.

Volatility Smiles & Smirks.

Volatility Skew Definition:

Using the Black Scholes option pricing model, we can compute the volatility of the underlying by plugging in the market prices for the options. Theoretically, for options with the same expiration date, we expect the implied volatility to be the same regardless of which strike price we use. However, in reality, the IV we get is different across the various strikes. This disparity is known as the volatility skew.

Volatility Smile.

If you plot the implied volatilities (IV) against the strike prices, you might get the following U-shaped curve resembling a smile. Hence, this particular volatility skew pattern is better known as the volatility smile.

The volatility smile skew pattern is commonly seen in near-term equity options and options in the forex market.

Volatility smiles tell us that demand is greater for options that are in-the-money or out-of-the-money.

Reverse Skew (Volatility Smirk)

A more common skew pattern is the reverse skew or volatility smirk. The reverse skew pattern typically appears for longer term equity options and index options.

In the reverse skew pattern, the IV for options at the lower strikes are higher than the IV at higher strikes. The reverse skew pattern suggests that in-the-money calls and out-of-the-money puts are more expensive compared to out-of-the-money calls and in-the-money puts.

The popular explanation for the manifestation of the reverse volatility skew is that investors are generally worried about market crashes and buy puts for protection. One piece of evidence supporting this argument is the fact that the reverse skew did not show up for equity options until after the Crash of 1987.

Another possible explanation is that in-the-money calls have become popular alternatives to outright stock purchases as they offer leverage and hence increased ROI. This leads to greater demands for in-the-money calls and therefore increased IV at the lower strikes.

Forward Skew.

The other variant of the volatility smirk is the forward skew. In the forward skew pattern, the IV for options at the lower strikes are lower than the IV at higher strikes. This suggests that out-of-the-money calls and in-the-money puts are in greater demand compared to in-the-money calls and out-of-the-money puts.

The forward skew pattern is common for options in the commodities market. When supply is tight, businesses would rather pay more to secure supply than to risk supply disruption. For example, if weather reports indicates a heightened possibility of an impending frost, fear of supply disruption will cause businesses to drive up demand for out-of-the-money calls for the affected crops.

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Learn About Volatility Skew.

Volatility skew refers to fact that options on the same underlying asset, with different strike prices, but which expire at the same time, have a different implied volatility .

When options first traded on an exchange, volatility skew was very different. Most of the time options that were out of the money traded at inflated prices. In other words, the implied volatility for both puts and calls increased as the strike price moved away from the current stock price -- leading to a " volatility smile ."

That is a situation in which out-of-the-money (OTM) options (puts and calls) tended to trade at prices that seemed to be "rich" (too expensive). When the implied volatility was plotted against the strike price (see image), the curve was U-shaped and resembled a smile. However, after the stock market crash that occurred in October 1987, something unusual happened to option prices.

There is no need to conduct extensive research to understand the reason for this phenomenon. OTM options were usually inexpensive (in terms of dollars per contract), and were more attractive as something for speculators to buy than as something for risk-takers to sell (the reward for selling was small because the options often expired worthless). Because there were fewer sellers than buyers for both OTM puts and calls, they traded at higher than "normal" prices -- as is true in all aspects of trading (i. e., supply and demand ).

Ever since Black Monday ( Oct 19, 1987), OTM put options have been much more attractive to buyers because of the possibility of a gigantic payoff. In addition, these puts became attractive as portfolio insurance against the next market debacle. The increased demand for puts appears to be permanent and still results in higher prices (i. e., higher implied volatility).

As a result, the "volatility smile" has been replaced with the "volatility skew" (see image). This remains true, even as the market climbs to all-time highs.

In more modern times, after OTM calls became far less attractive to own, but OTM put options found universal respect as portfolio insurance, the old volatility smile is seldom seen in the world of stock and index options. In its place is a graph that illustrates increasing demand (as measured by an increase in implied volatility (IV) for OTM puts along with a decreased demand for OTM calls.

That plot of strike vs. IV illustrates a volatility skew . The term "volatility skew" refers to the fact that implied volatility is noticeably higher for OTM options with strike prices below the underlying asset's price. And IV is noticeably lower for OTM options that are struck above the underlying asset price.

NOTE: IV is the same for a paired put and call. When the strike price and expiration are identical, then the call and put options share a common IV. This may not be obvious when looking at option prices.

The inverse relationship between the stock price and IV is a result of evidence that shows us that markets fall much more quickly than they rise.

There currently exist a number of investors (and money managers) who never again want to encounter a bear market when unprotected, i. e., without owning some put options. That results in a continued demand for puts.

The following relationship exists: IV rises when markets decline; IV falls when markets rally. This is because the idea of a falling market tends to (often, but not always) encourage (frighten?) people to buy puts -- or at least stop selling them. Whether it is increased demand (more buyers) or increased scarcity (fewer sellers), the result is the same: Higher prices for put options.