Warrants: keeping track with the “Greeks”

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  Serge Nussbaumer
  Chefredaktor

The “Greeks” are sensitivity measures from classical option theory. They show how the price of a warrant changes if a certain influencing factor changes. They therefore help investors to better assess the often chaotic price behavior of warrants.

Delta: The price sensitivity

Let’s start with the “Greek” that receives the most attention: the delta. This shows how much the price of a warrant changes if the price of the underlying moves by one unit. For a call warrant, the delta is generally between 0 and 1, for a put warrant between -1 and 0. Let’s assume a call on a Swiss share has a delta of 0.4: this means that if the share price rises by CHF 1.00, the value of the warrant rises by CHF 0.40. For a put on the same share, let’s say the delta is between 0 and 1. A put on the same share is assumed to have a delta of -0.6. If the share falls by CHF 1.00, the value of the put rises by CHF 0.60 (subscription ratio 1:1 in each case). In practice, the delta is important as it provides information on how sensitively a warrant reacts to price movements in the underlying. It can also provide an indication of the probability of a warrant being “in the money” at expiry, i.e. having an intrinsic value. As a general rule, the higher the intrinsic value of a warrant, the closer its delta is to 1 (call) or -1 (put). But be careful: Like all other “Greeks”, the delta is always only a snapshot at the respective point in time. It changes with every price movement of the underlying. The next “Greek”, the gamma, provides information on the extent to which the price performance of the underlying moves the delta.

Gamma: The delta of the delta

The gamma measures the change in the delta if the price of the underlying increases or decreases by one unit. Let us assume that a call warrant on a share has a delta of 0.5 and a gamma of 0.1. If the share now rises by CHF 1.00, the delta increases to 0.6. In general terms: If the price of the underlying changes by one unit, the delta changes by the gamma. A high gamma means that the delta reacts very sensitively to price movements in the underlying. The gamma is particularly high for warrants that are “at-the-money”. This means that the price of the underlying is quoted close to the strike of the warrant. In this case, even small price movements in the underlying can lead to large changes in the delta and thus in the price of the warrant. With the help of the gamma, investors can, for example, estimate the extent to which a warrant quoted “at the money” builds up additional leverage if the underlying goes into the money, or how much leverage is lost in the opposite case.

Vega: The volatility sensitivity

This “Greek” provides information on how strongly the price of a warrant reacts to changes in the implied volatility of the underlying. If the expected fluctuation margin of the underlying increases, the warrant becomes more valuable – regardless of whether it is a call or a put (and vice versa). For example, if the vega of a warrant is 0.08, an increase in the implied volatility of the underlying by one percentage point (all other things being equal) leads to an increase in the value of the warrant of CHF 0.08 (with a subscription ratio of 1:1). In practice, price slumps often lead to a rapid increase in the expected volatility, as such corrections are usually quick and abrupt. This results in exciting trading opportunities. Investors who assume that a company will surprise negatively with its quarterly figures, for example, can profit twice with a put warrant with a high vega: firstly from the price losses of the underlying asset and secondly from the volatility-related increase in the value of the warrant. If, on the other hand, you buy warrants in times of decreasing volatility, you should ensure that the vega is as low as possible.

Theta: The loss of time value

Theta describes the time value loss of a warrant, i.e. its loss in value over time. The closer the expiry date approaches, the faster the time value of a warrant falls. Example: A theta of -0.02 means that the price of the warrant falls by an average of CHF 0.02 with each passing day – provided that all other influencing factors remain constant. As a rule, the influence of theta is strongest for “at the money” listed warrants with a short remaining term. In contrast, “out-of-the-money” warrants hardly show any loss of time value. Their theta is low.

Rho – The interest rate sensitivity

Rho indicates how sensitively the price of a warrant reacts to changes in the general interest rate level. If market interest rates rise, call warrants tend to become more valuable, while the value of put warrants falls. Example: If the market interest rate rises by one percentage point and the Rho of the call warrant is 0.04, its value increases ceteris paribus by CHF 0.04. In practice, the Rho is of rather minor importance, as warrants have a manageable term during which drastic shifts in the interest rate level are rather unlikely.

Omega: Not a classic “Greek”, but useful!

The omega is often also counted among the “Greeks”, but strictly speaking this is not correct. This indicator shows the effective leverage effect of a warrant. For example, if a warrant has an omega of 5, its price rises by 5% if the underlying rises by 1% – and falls accordingly if it falls. The omega combines the delta and the theoretical leverage. The formula is: omega = delta x (price of the underlying asset/price of the warrant). As already mentioned several times, the omega only applies to the period under review. The leverage effect can therefore increase or decrease.