## Delta in structured products

The delta measures the price sensitivity of an option for a given change in the underlying asset's price. In other words, it shows how much an option's price will rise or fall if the price of the underlying asset moves. The following paragraphs focus on the change in the delta value in relation to time to expiration in structured products. We will examine four different structured products: capital guaranteed notes, reverse convertibles, bonus certificates and certificates.

###### The delta of calls and puts

The graph to the right shows the values that the delta can take for calls (white line) and puts (green line) in function of the asset's price. Suppose that the strike for both call and put is 100% (at-the-money); the call's delta is worth 50% and the put's -50%. When the asset's price increases, the call's value increases as well, tending towards 1 (or 100%). At the same time, the put's delta also increases, tending towards zero. The reverse reasoning applies when the value of the asset decreases: the call becomes out-of-the-money and its delta decreases to tend towards zero, while the put's delta decreases as well to tend towards -1 (or -100%). Thus, a plain vanilla call's delta can assume values between 0 and 1, while put's delta can have values between 0 and -1.

For example, if a share is worth CHF 100 and the call option on that share with a delta of 40% is worth CHF 5, the value of the call option will increase to CHF 5.40 if the share gains CHF 1 (eightfold leverage).

The more an option is in the money, the higher the delta tends to be. On a payoff diagram, the delta can be approximated by the slope of the curve. A 45° line represents a delta of 1. A horizontal line represents a delta of zero. In essence, the steeper the slope, the higher the delta.

###### Capital guaranteed products

Classical capital guaranteed products usually consist of a money market investment and a call option (the option is a put if the participation is on the downside of the underlying asset). The product’s delta is largely determined by the call option. Products without cap have usually a delta around 0.5 (or 50%) when issued. This causes sometimes some disappointment with the investor, as the product, even if promising 100% participation at maturity, achieves only half that number at inception. During the life of the product, the delta varies according to the performance of the underlying in relation to the strike of the call. If the underlying rises in value, the delta rises, and the participation accordingly. As the product approaches its maturity, the delta tends towards 1 if the underlying has risen (the participation tends to 100% as written in the termsheet) or zero, if the underlying has a flat or negative performance. if the product features a cap, a knock-out barrier or any other type of exotic option, the delta will be different and largely depends on the option type.

###### Reverse Convertibles

With a reverse convertible, the investor forgoes part of the potential positive performance of the underlying asset in return for a high coupon and, in the case of a barrier reverse convertible, some conditional protection. The risk is that the investor may have to accept the underlying asset at a predefined level. The payoff profile can be replicated with a zero coupon bond and a short put option. The delta is solely determined by the put option. It is usually around 0.5 at inception, falls towards zero if the underlying strongly increases in value, and rises towards 1 if the underlying asset falls strongly. The reverse convertible thus becomes a bond-like product with rising underlying asset prices and behaves like the underlying asset itself if its price falls strongly. The investor should never be fooled in thinking that a reverse convertible is a replacement for a bond just because it pays a high coupon. The investor should keep in mind that the higher the reverse convertible’s coupon is in relation to the risk free rate, the higher the associated risk becomes.

###### Bonus Certificates

Bonus certificates are suitable for optimistic but risk-averse investors. They provide conditional capital protection (*not *guarantee) and at the same time offer unlimited earnings potential. A bonus certificate is constructed through a call option with a zero strike and a down-and-out put option. The delta is around 0.95 at inception. Note that the delta works both ways: thus, the product will move nearly 1:1 to the upside as well as to the downside early in its life. The conditional protection works only close to and at maturity. Primarily for this reason, we advise to keep the lifetime of bonus certificates as short as possible; no investor likes to wait for years and years for the conditional capital protection to have an effect. Having a 50% barrier is of little use, if after 1 year the underlying dropped by 25% and the product’s mark-to-market value trades around 78% and 4 years remain until maturity. Most investors will get impatient and ditch the product. During the life of the product, the delta can vary wildly according to the time remaining until maturity and the performance of the underlying in relation to the strike and the barrier. Close to maturity, if the spot is close to the barrier, the delta can become even greater than 1 before knocking it. This is a particularity of exotic options featuring a barrier: the delta can rise above 1. It tends to zero if the barrier is still far away but the spot below the strike of the down & out put. It tends towards 1 if the spot is above the strike.

###### Certificates

As certificates match the performance of the underlying asset(s) on a one-to-one basis, their delta is always 1, irrespective of the time to expiration, as this product does not have any optionality.