Volatility (finance)

Volatility (Latin volatilis, flying ',' volatile ' ) refers to statistics in general, the variation of time series.

Volatility in economics

The term volatility is often found in economics use. In financial mathematics, it is a measure of the fluctuation of financial market parameters such as stock prices and interest rates. Volatility is defined as the standard deviation of changes (also returns, returns) of the considered parameter and often serves as a measure of risk.

The change in value can be defined in different ways. We distinguish:

• Absolute changes

• Relative changes

• Logarithmic or logarithmic changes ( cf. continuous compounding )

In addition, the time interval must be defined for which the changes are defined. Volatilities are usually expressed as the standard deviation of annual changes (so-called annualized volatilities).

Absolute changes in value are for example used when volatility is to be determined by interest rates. Relative and logarithmic value changes differ by small changes little and used eg for stochastic modeling of stock prices (see Ito process). Go a log of changes in value in the option pricing model of Black & Scholes.

Historical Volatility

As a historical volatility is defined as the volatility that you calculate from the time series of historical changes in value. In value-at -risk models for measuring market risk, see historical volatility as an estimator for future fluctuation input.

Historical volatility is classified as a Lagging Indicator.

Implied Volatility

In contrast to historical volatility, implied volatility is not based on historical time series. It is derived rather from the market prices of options. The implied volatility is the volatility of the underlying asset of an option which, when used in an option pricing model (eg Black-Scholes model), just gives the observed market price of the option.

For standard stock indexes own volatility indices are published that measure the implied volatility of the underlying.

Volatility in politics

The concept of volatility (English " volatility " ) is a native of the physics term used to describe the instability of party preferences of voters in a party system. ( cf. Schultze / Nohlen, 2004, 1114 ) appeared in 1979 to a drafted by Mogens N. Pedersen article in the scientific magazine " European Journal of Political Research " on "The Dynamics of European Party Systems: Changing Patterns of Electoral Volatility ," in which he further reflects the fluctuations of party preferences of the electorate. Volatility is the German translation for the English word ' volatility ' (Eng. fluctuation, inconstancy ) ( cf. Schultze / Nohlen, 2004, 1114 ), which in turn from the Latin word volatilis ' derives (German flying, volatile). In political science, the volatility of the volatility or change in the voting decision of a person stands with regard to a particular political party between two temporally spaced options, so a change in the inputs in an election by one or more persons with a passive right to vote in a second choice to a later. The assumptions for volatility, ie the " volatility or instability with respect to the choice of a particular political party " ( Schmidt, 1995, 1030 ) are the presence of free and fair elections and a temporary separation of powers, that is, elections are held on a regular basis. Only then it is possible for the electorate to choose a political party or to change his voting decision in a second ( subsequent) choice again. Volatility is divided in political thinking into two groups: one in which, net volatility ', on the other, in which large volatility '. The ' net volatility ' specializes, in the insgesamten change the voters voting shares, one can speak in this sense of the long shot volatility or the "aggregate volatility ". The, large volatility ' is concerned, however, with the other effectively voting decision on the individual micro - level. Examples of an effective choice decision are, for example, another choice decision, the abstinence in the election, so that not voting, and education and entrance into and out of the electorate (See Ladner, 2004.106 ). Volatility is usually calculated by the Pedersen index. This volatility can be calculated either at the level of the electorate, or at the level of the political arena. Depending on which level is selected, either the fluctuation on the basis of the popular vote ( level of the electorate ) or by the change of the seats in parliament ( parliamentary level ) must be taken into account. It means the measurement of volatility for Pedersen following: "The measure of volatility tells to what extent party strength is being real located from one election to the next in between losing and winning parties. " ( Pedersen, 1990, 199)

To calculate the volatility Morgan N. Pedersen has worked to the following general formula:

Total volatility

Here, n is the number of parties in the analysis of a political system. Vit represents the share of the vote or the number of mandates t at the starting point and Vi (t 1 ) for a subsequent examination at the measurement point t 1 ( Ladner, 2004, 99). Furthermore, it is possible to perform the measurement of Total volatility for multiple parties. The sum for each party from Vit -Vi (t ​​ 1) is created, added and then divided by 2 so that you get the long shot volatility for one -party system. ( Ladner, 2004, 99)

In the following formula, | PiV |, | PJV |, | PkV | and | PeV | for various parties.

Total volatility ( for n parties )

( cf. Bartolini / Mair, 1990, 28) In addition to the volatility of the long shot There is also the opportunity to study the fluctuations in electoral blocs or between party blocks. A distinction is made in the measurement of volatility, inter-block volatility and intra-block volatility. In the inter-block volatility is the fluctuation of voters interests of the " electoral blocs " and in the intra-block volatility to the fluctuation of voters shares in the " electoral blocs ". To measure the intra-block volatility and inter-block volatility dividing the parties in their respective political camps. One possible classification it would be, for example, to locate the parties on a left-right scale, and to examine the extent to which sway the election results to the left or right on the scale. A second option would be for example to divide the parties according to government participation and non - participation in government and so determine the fluctuations in elections between the current government and opposition. The volatility for each party is calculated and the volatility results from the parties at the different blocks with each summed and then divided by 2. ( Cf. Bartolini / Mair, 1990, 28 /29) is problematic for use with the Pedersen index, that can not be determined exactly which parties win votes and lose what parties which; level of both can not be determined to what extent the electorate shift between the parties or compensated. For the long shot volatility, this is not serious, for the individual level but this may be of great importance. Also it is not possible to develop the basis of a high or a low volatility statements about the stability of a party system. ( Ladner, 2004, 105/106 )

Despite these problems between volatility at the individual micro-level and aggregate level is to start from a relatively high correlation value of 0.74. ( Ladner, 2004, 106). The Pedersen index can thus "is a strong and long-term indicator of the change in the party system, in addition to party identification, the number of members and the number of parties " ( Schultze, 2002, 1114 ) are counted.

Volatility in the natural sciences

In the natural sciences volatility means the measure of the volatility, or the tendency to volatilization of substances in gases.

Volatility in software engineering

For projects under version control, the frequency of changes to the files is referred to as volatility. This is considerably lower than for files in structure definitions and header files, the application logic, etc. objects contain. Functions and requirements (for example, since the last release ) covered by sources with high volatility are to be examined more intensively in conducting a regression testing, because you have to assume that the less volatile source areas of work "stable". However, this does not guarantee that rarely changed source areas work more stable.