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The Volatility Smile

Option markets are multidimensional, in fact, options spreads can be created using different strikes, different maturities or different type of options (calls / puts). Besides, option traders cannot track instantaneous price changes on the entire option chain, hence, it is easy to derive that the most important factor in option trading is not the price of the option itself. The variable that has to be accurately tracked and monitored at all times is, in fact, what drives and determines the price of the option: volatility. In reality, there are different types of volatilities but the one extracted from option premiums is called implied volatility (the volatility extracted from futures prices is instead referred to as realized volatility) and its shapes and fluctuations are crucial to any market player involved in options trading. The present research will try to describe the dynamics of the implied volatility shape and to analyze its most common evolutions: Smile, Smirk and Forward Skew. In particular, the implied volatility figures used in the present examination have been extracted from front month WTI option premiums traded on the 30th of August 2013 which expire in October. All calculations and charts have been respectively performed and created with the HyperVolatility Option Toolbox. The following chart displays the so–called volatility smile:

Volatility Smile

(Source: HyperVolatility Option Toolbox)

As we can see from the above reported graph, the curve is higher at the extremes but rather low in the middle (bear in mind that the At–the–Money strike was $107.5). This is the typical shape for a front month implied volatility curve where the high demand for ITM calls and OTM puts as well as for ITM puts and OTM calls drives the volatility higher. In many cases, you will hear that the volatility for Out–of–the–Money options is higher but such statement is clearly incorrect because without further specification it implies that only OTM puts and calls experience such high volatility. The chart evidently shows that the volatility for ITM and OTM options is higher but, for obvious reasons, the volatility for the strike where a call option is In–the–Money will be almost as high as the volatility for the Out–of–the–Money put option and vice versa. Consequentially, saying that Away–from–the–Money options (both calls and puts) have a higher implied volatility than At–the–Money options is without a doubt the most correct statement. The most natural questions at this point would be: Why? What does a smile–shaped curve tell us?

The most obvious thing to say is that the volatility on AFTM options is higher because investors tend to trade them more often and they consequently push the volatility on the upside. The reason why investors buy wings is that ITM options have more intrinsic value than the ATM ones while OTM options have more extrinsic value than an option struck At–the–Money. Consequentially, the presence of an implied volatility smile–shaped curve is typical of more speculative markets. The smile suggests that, when large volatility shifts happen, many market players rush to buy OTM options for speculative reasons while ITM options are primarily purchased to stabilize portfolio gains. The next chart shows how the curve moves:

Volatility Smile - Dynamics

(Source: HyperVolatility Option Toolbox)

Many researches on implied volatility curve dynamics showed that the 75% of volatility changes can be defined by a total shift, up or down, of the entire curve as you can see from the chart. A further 15% of the movements consist of curve twisting (the right hand side of the curve goes deeper down while the left side gets pulled on the right or vice versa) while the remaining 10% is the product of a change in convexity (wings getting wider or tighter).

Smile–shaped curves are frequently found in equity index options, stock options and popular commodities / currencies (Euro, WTI, Gold, etc). Nevertheless, it is worth noting that the shape of the curve can even evolve over time. This concept can be better explained by looking at the following chart:

Volatility Smirk

(Source: HyperVolatility Option Toolbox)

The smirk is a particular volatility profile where ITM calls and OTM puts are priced with a much higher implied volatility. This phenomenon is commonly found in equity markets and risky assets. In this simulation the ATM strike is 116 and its volatility is 13.1% but OTM puts and ITM calls are much more expensive because they are trading above the 70% level. As previously mentioned, the implied volatility curve can change and evolve and a volatility smile can turn into a smirk if investors, traders and market players are expecting a market crash or if the plunge in price has already happened. Smirks are simply telling us that lower strikes are more traded than higher strikes and OTM puts as well as ITM calls are being heavily traded. If the market is heading south, a smile would easily evolve into a smirk because of the great buying pressure generated by market players rushing to buy OTM puts to protect their portfolios. The purchase of ITM calls, even during market crashes, makes sense because ITM call options have already an established intrinsic value and they have the highest probability to expire In–the–Money; in other words they are safer. However, in the event of market downtrends the evolution of a volatility smile into a smirk would predominantly be caused by the large buying volume on OTM puts.

The Volatility smile, nevertheless, can go through another metamorphosis whose final output is the so–called forward skew:

Volatility Forward Skew

(Source: HyperVolatility Option Toolbox)

The forward skew is nothing but a reversed form of smirk, in fact, the volatility here tends to become higher for ITM puts and OTM calls. This type of curve is more frequently found in commodity markets, particularly agricultural products, than equity indices or stock options. Even in this case the increase in volatility is provoked by an augment in demand for these options. However, the strong buying pressure concentrated on OTM calls is often the main cause of such shape. Let us break it down. Many players in commodity markets are commercials (mining and energy companies, grain / wheat / sugar / coffee producers) and therefore a disruption in the supply chain of a particular commodity can generate serious problems. A shortage in oil supply due to geopolitical variables, a disappointing crop due to a frost or to challenging meteorological conditions, continuous strikes in a particularly large mine are all factors that would force companies to buy as quickly as possible the commodity they need in order to lock in the order. Consequentially, the remarkable buying pressure on OTM calls would inevitably drive their price up and that is why the implied volatility of higher strikes is more elevated than others.

Let us now summarize the main concepts in order to avoid confusion:

1) An implied volatility smile means that Away–from–the–Money options have a higher implied volatility than At–the–Money options

2) Implied volatility smile–shaped curves are typical of highly speculative markets

3) Many researches on implied volatility curve dynamics showed that the 75% of all volatility changes consist of a shift, up or down, of the entire curve

4) Smile–shaped curves are frequently found in equity index options, stock options and the most popular commodities / currencies

5) The smirk is a particular volatility profile where ITM calls and OTM puts are priced with a much higher implied volatility

6) Volatility smile curves can turn into a smirk if investors, traders and market players are expecting a market crash or if the plunge in price has already happened

7) The forward skew is a reversed form of smirk, in fact, the volatility here tends to become higher for ITM puts and OTM calls

8) The forward skew curve is more frequently found in commodity markets (particularly in agricultural products)

9) The formation of a forward skew curve is often the consequence of a shortage in the supply chain due to transportation issues, geopolitical problems, adverse meteorological conditions, etc

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