Structured Products

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Skew - Smile

Financial options are influenced by many factors, among others implied volatility. Implied volatility expresses the level of uncertainty that the market participants attribute to a risky underlying asset for a given maturity in the future. A higher uncertainty will result in a higher volatility, which in turn will increase the price of the options. The reverse is true for less uncertainty. An observable fact in the market is that options on an identical asset for a given maturity have different volatilities. This phenomenon is called the smile or the skew.

 In a true smile, options with an at-the-money strike are priced with a lower volatility than out-of-the-money and in-the-money volatility strikes. Such market occurrences are observable in the FX market. A typical smile as in the FX market is represented by the picture on the right.

For example, suppose an at-the-money call option on a given asset and with a given maturity has an implies volatiltiy of 12%, and that its delta amounts to 50%. Imagine now that another call option with the same maturity on the same asset is priced with an implied volatility of 14% but its strike is out-of-the-money and its delta is 40%. A third option with a strike in-the-money and a delta of 60% is also priced with a volatility of 14%. Table 1 summarizes the values:




Table 1: Smile

In-the-money call



At-the-money call



Out-of-the-money call




Options of other markets, like the stock market, are priced slightly differently. They have a skew. In a skew, out-of-the-money strikes are priced with a lower volatility than at-the-money strikes, and in-the-money strikes are priced with a higher volatility. The skew is also referred to as a crooked smile. A typical skew as encountered in the equity markets is shown on the picture below and to the right; the horizontal scale represents the value of the underlying asset (an equity index), the spot price being 3'312 at the time the picture was taken.

What moves market participants to change the volatility of any asset according to an option’s strike? The answer to this question lies in a combination of market participant power, behavioural finance and offer and demand.

In the FX market, sudden FX pair price movements can be triggered by central banks when they decide to lower or raise rates. The "normal" level of the volatility is not high enough to cover the price swings of a normal FX pair. Market participants price the extreme movements in the option market with higher volatility the further away the strike of the option is agianst the current (forward) spot. Natural catastrophes, wars and economical shocks can send one or the other currency plunging or rocketing against another, depending on what happened where. These extreme events, while unlikely, happen every once in a while and also contribute to traders pricing the volatility of "extreme" strikes at higher levels. Their reasoning is that if the FX pair reaches a far out-of-the-money strike or a deep in-the-money strike, the volatility will have increased anyway, so might as well price the volatility at a higher level.

On the equity market, the situation is a little diferent. While stocks do crash once in a while, they seldom crash to the upside (unless when they are a takeover target). So the equity market prices out-of-the-money strikes with lower volatility than in-the-money strikes. The resulting skew is also a result of a demand overhang of puts and an offer overhang for calls. It can be empirically observed that large pension funds and insurers often sell out-of-the-money calls in order to finance the purchase of protective puts.

For structured products, the existance or the absence of a smile or skew, as well as its level, has strong implications. For instance, placing a cap on a capital guaranteed product based on a stock index will yield less value when the skew is pronounced. Since the placing of a cap is equal to selling a call, the implied lower volatility for the out-of-the-money strike will yield lower premiums, making the whole product less attractive. On the other hand, a barrier reverse convertible will profit from a strong skew, since the barrier will be placed at lower strikes priced with a higher volatility. 

To conclude, the volatility smile or skew of the underlying asset's options matter when choosing a product. It is a factor to take into account when considering capped products or those featuring a barrier either to the upside or to the downside. To observe the skew of a particular asset's options, find an internet site that calculates and shows the volatility of an option series or ask your bank representative.