## Options are the right to purchase something at a specific price

The standard forms (plain vanilla) of an option are the call and put options. The option's buyer has the right - but not the obligation - to buy or sell a certain quantity of the underlying asset at a predetermined strike price on specific exercise dates. The seller of the option receives the option's purchase price, and he is obliged to sell or buy the underlying asset at the previously determined price.

A distinction is made between two types: physical delivery and cash settlement. If physical delivery is agreed upon, one counterparty (in the case of a put option, the holder, in the case of a call option, the seller) delivers the underlying asset. In contrast, the other counterparty pays the purchase price.

In the case of a cash settlement, the seller pays the difference between the price and the market price of the underlying asset on the respective date to the option holder. Usually, the reverse case, in which the holder pays to the seller, cannot occur, as the holder does not exercise the option in this case.

The holder's economic advantage is the same in both cases, apart from the transaction, storage, and delivery costs.

## Different option types determine when an option can be executed

In addition to the standard options, there are exotic options whose payout profile depends not only on the difference between the share price and the exercise price. Depending on the exercise dates, a distinction is made between

- European option: the option can only be exercised on the maturity date;
- American option: the option can be exercised on any trading day before the maturity date;
- Bermuda option: the option can be exercised on several predetermined dates.

## Options can be bought for many different assets

Options can be bought on basically anything traded and even weather! The most common options are:

- Shares
- Indices
- Currencies
- Bonds
- Swaps (so-called swaptions)
- Exchange-traded fund (ETF)
- Raw materials
- Food
- electrical energy

## The risk of an option is determined through the so-called "Greeks"

The "Greeks" describe different dimensions of risks related to options, and these variables are associated with Greek symbols.

### Delta

The delta is a sensitivity index that indicates the influence of the underlying asset's price on the value of the option. It is mathematically the first derivative of the option price after the underlying asset price. For example, a delta of 0.5 means that a change in the underlying asset of €1 (in linear approximation) causes a change in the option price of 50 cents. The delta is significant in so-called delta hedging.

### Gamma

The gamma of an option indicates how much its delta (in linear approximation) changes if the price of the underlying asset changes by one unit and all other variables do not change. Mathematically, the gamma is the second derivative of the option price after the underlying asset price. For the option holder (i.e., for both long call and long put), gamma ≥ is always 0. This key figure is also considered in hedging strategies in the form of Gamma hedging.

### Theta

The theta of an option indicates how much the theoretical value of an option changes if the remaining time to maturity is shortened by one day and all other variables remain constant. For the owner of the option, the theta is usually negative. Hence, a shorter remaining term always means a lower theoretical value.

### Vega

The vega (sometimes also lambda or kappa, since vega is not a letter of the Greek alphabet) of an option indicates how much the value of the option changes if the volatility of the underlying asset changes by one percentage point and all other variables remain constant.

### Rho

The rho of an option indicates how much the option's value changes if the risk-free interest rate in the market changes by one percentage point. The rho is positive for call options and negative for put options.

### Leverage

The leverage is calculated by dividing the underlying asset's current price by the option's current price. If the option relates to a multiple or fraction of the underlying asset, this factor must be considered accordingly in the calculation. This is referred to as the subscription ratio.

### Omega

By multiplying the delta by the current lever, a new lever size is obtained, usually found in the price tables under the designation Omega or "lever effective". Thus, an option with a current leverage of 10 and a delta of 50% has "only" an omega of 5, so the ticket increases by about 5% if the base increases by 1%. However, it should be noted that both the delta and the omega and most other key figures are constantly changing. Nevertheless, the omega offers a relatively good picture of the chances of the corresponding option.

## Summary: Options are not for the average Joe

As you can see, there are many things to consider when trading options. Also, options have maturity dates and therefore are not suitable for buy-and-hold strategies. Instead, they require active and knowledgeable management.