What is the Theta in Options Trading?

What is the theta of an option? Options Greeks like theta are sensitivity metrics used to try to explain the pricing of options. Option Greeks allow investors to assess how certain factors affect the price of the option.

The theta indicates the extent to which the option price falls when the remaining life of the option decreases by one day. All other factors influencing the price of the option remain unchanged. Thus, the option theta captures the decline in fair value of options. As the remaining term of an option becomes shorter and shorter, the time value expires. The decline in fair value tends to be slow at first and increases exponentially at the end of the option’s term.

Theta and time value loss in practice

The largest decline in fair value with a significant exponential decrease can be observed in the last 30 days of the option term. The change in the theta thus becomes larger. It is important to understand that the decline in fair value is a continuous process.

The option theta can therefore also change the option price during the course of a day, with the largest time loss in fair value occurring in the period between the closing of the exchange on one day and opening on the following day. Usually, the theta is given as the “weekly theta”. For extremely short-running options, however, it is useful to use the “daily theta”.

In the case of very long-running options, the fall in fair value at the beginning of the term is almost the same, regardless of whether the option is quoted in, at or out of the money. Differences only become apparent as the remaining term decreases. Options that are quoted “at-the-money” usually show the strongest change in the theta, i.e. a higher decline in fair value.

The reason is that the probability that the underlying asset will still change very strongly decreases as the remaining time to maturity gets shorter.

The implied volatility also has an influence on the theta. A higher implied volatility results in a higher theta.

Calculation of the option theta

The theta is calculated by converting the option price formula to Black Scholes. If you trade with options, you will find the always current value for the theta as well as for the other option greens in the broker’s trading lists. The values are continuously recalculated.

The option theta can be given as a percentage (e.g. 4%) or as an absolute number (e.g. -0.04). For call options, the value is greater than zero. Often a negative value is also specified. This is merely to illustrate the loss in value of the option when the remaining term is shortened. A weekly theta of 4% means that the time value decreases by 4% within one week.

Even with put options, the value is predominantly greater than zero. In the case of European options that can only be exercised at the end of the option term, the value can be negative in the case of deep-in-the-money options.

Conclusion

The theta is used to determine by how much the option price falls if the remaining term of the option is reduced by one day. The shorter the remaining term of the option, the greater the decrease in fair value. For example, if you compare two options on the same underlying asset but with different terms, the decline in fair value of the shorter-running option is higher than that of the longer-running option. The theta of the shorter-running option thus assumes a higher value. For both, however, the time value expires exponentially shortly before the end of their respective terms. The buyer of an option thus makes a loss, even if the price of the underlying asset does not change at all. For the seller of an option, for example, who uses an option strategy such as covered calls, this in turn means a profit.


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