# volatility

In statistics, volatility ( Latin volatilis , 'flying', 'fleeting') generally describes the fluctuation of time series .

## Volatility in Economics

### General

In risk management, economics investigates a large number of changing economic parameters such as share prices , exchange rates , market values , interest rates , returns or metal values ( gold price , silver price ). Their fluctuations over time can involve a price risk for financial products for market participants . In financial mathematics , volatility is a measure of these fluctuations.

The volatility is defined here as the standard deviation of the changes (including returns) of the parameter under consideration and is often used as a measure of risk . However, it is not an ideal risk measure because it only provides information about the fluctuation range of an underlying asset, but does not provide any further information about the distribution function of the price fluctuations .

The change in value, on the basis of which the volatility is calculated, can be defined in various ways. One differentiates:

• absolute changes
${\ displaystyle \ mathrm {{\ ddot {A}} change} = {\ text {value}} _ {t1} - {\ text {value}} _ {t0}}$
• relative changes
${\ displaystyle \ mathrm {{\ ddot {A}} change} = {\ frac {{\ text {value}} _ {t1} - {\ text {value}} _ {t0}} {{\ text {value }} _ {t0}}}}$
${\ displaystyle \ mathrm {{\ ddot {A}} change} = \ ln ({\ text {value}} _ {t1}) - \ ln ({\ text {value}} _ {t0}) = \ ln {\ frac {{\ text {value}} _ {t1}} {{\ text {value}} _ {t0}}}}$

with as the time interval with which the variable base variable is measured. “Annualized volatilities” relate e.g. B. on the standard deviation of annual changes. ${\ displaystyle (t1-t0)}$

Absolute changes in value are used, for example, when the volatility of interest rates is to be determined. Relative and logarithmic changes in value hardly differ in the case of small changes and are e.g. B. used for stochastic modeling of share prices (see Ito process ). Logarithmized changes in value are included in the Black & Scholes option pricing model .

The past volatility is the "historical realized volatility". In contrast, the implied volatility is a quantity that can be derived from option price models (e.g. the Black-Scholes model ) from the market prices of options (i.e. implied by the option prices). Implied volatilities can be interpreted as an expression of the market opinion on future market price fluctuations.

### Historical volatility

Historical volatility is the volatility that is calculated from time series of historical changes in value. In value-at-risk models for measuring market price risks , historical volatilities are used as estimators for future ranges of fluctuation.

The historical volatility is classified as a lagging indicator .

### Implied volatility

In contrast to historical volatility, implied volatility is not based on historical time series. Rather, it is derived from the market prices of options . The implied volatility is the volatility of the base value of an option which, when used in an option price model (e.g. Black-Scholes model ), precisely yields the observed market price of the option.

Volatility indices that measure the implied volatility of the underlying are published for standard stock indices .

## Volatility in Politics

The term volatility is a term derived from physics that is used to describe the instability of the party preferences of an electorate in a party system. In 1979 an article was published by Mogens N. Pedersen in the scientific magazine "European Journal of Political Research" under the title "The Dynamics of European Party Systems: Changing Patterns of Electoral Volatility", in which he looked more closely at the fluctuations in party preferences Electorate in the European party system. In political science, volatility stands for the inconsistency or change in a person's voting decision with regard to a certain political party between two elections that are temporally separated, i.e. a change between the input for one election by one or more persons entitled to vote and that for a second election at a later date. The premises for volatility are the existence of free and fair elections as well as a temporary separation of powers, i. This means that elections are held regularly. Only then is it possible for those entitled to vote to vote for a political party or to change their voting decision in a second (later) election. In political thinking, volatility is divided into two groups: on the one hand into 'net volatility' and on the other hand into 'gross volatility'. The former deals with the overall change in the proportion of votes cast; in this sense, one can also speak of total volatility or "aggregate volatility". Whereas the 'gross volatility' deals with the effectively different choice decision on the individual micro level. Examples of an effective other voting decision are, for example, another voting decision, abstinence from voting, i.e. not voting, and leaving and joining the electorate. Most volatility is calculated using the Pedersen index. This can calculate the volatility either at the level of the electorate or at the level of the political arena. Depending on which level was chosen, one must either take into account the fluctuation based on the votes (level of the electorate) or based on the change in the seats in parliament (parliamentary level). For Pedersen, measuring volatility means the following: "The measure of volatility tells to what extent party strength is being reallocated from one election to the next between losing and winning parties."

To calculate the volatility, Pedersen developed the following general formula:

${\ displaystyle {\ text {Total volatility}} = \ sum _ {i = 1} ^ {n} {\ frac {\ vert V_ {i} (t) -V_ {i} (t + 1) \ vert} {2}}}$

Here n stands for the number of parties in the examined political system. Vit stands for the proportion of voters or the number of mandates at starting point t and Vi (t + 1) for a later investigation at measuring point t + 1. It is also possible to measure the total volatility for several parties. The sum that arose from Vit -Vi (t + 1) for each individual party is added and then divided by 2, so that the total volatility for a party system is obtained.

In the following formula, | PiV |, | PjV |, | PkV | and | PeV | for different parties.

Total volatility (for n parties)

${\ displaystyle = {\ frac {| PiV | + | PjV | + | PkV | + | PeV | + \ dots + | PnV |} {2}}}$

In addition to the total volatility, it is also possible to examine the fluctuations in party blocks or between party blocks. When measuring volatility, a distinction is made between inter-block volatility, which is the fluctuation of the proportion of voters between the “party blocks”, and intrablock volatility, which is the fluctuation of the proportion of voters within the “party blocks”. To measure the intrablock volatility or interblock volatility, the parties are divided into the respective political camps. One possible classification is e.g. For example, to locate the parties on a left-right scale and to examine the extent to which the election results differ on the left and right on the scale. A second possibility is e.g. B. to divide the parties according to government participation and non-government participation and thus determine the development of the relationship in elections between the current government and the opposition. The volatility is calculated for each individual party and the volatility results of the parties are summed up in the various blocks and then divided by two. The problem with working with the Pedersen Index is that it cannot be precisely determined which parties win votes and which parties lose them. In addition, it cannot be determined to what extent the electorate shifts or evened out between the parties. This is not severe for total volatility, but at the individual level it can be very important. It is also not possible to use high or low volatility to develop statements about the stability of a party system.

Despite these problems between volatility at the individual micro level and the aggregate level, a relatively high correlation value of 0.74 can be assumed. The Pedersen Index can therefore be rated “as a strong and long-term indicator for the change in the party system, in addition to party identification, the number of members and the number of parties”.

## Volatility in science

In the natural sciences, volatility means the degree of volatility or the tendency to volatilize substances in gases.

## Software engineering volatility

For version controlled projects, the frequency of changes to the files is known as volatility. This is significantly lower for structure definitions and header files than for files containing application logic, objects, etc. Functions and requirements that are covered by sources with high volatility (for example since the last release) should be examined more intensively when performing a regression test, because one must assume that the less volatile source code areas function “stably”. However, this does not guarantee that source code areas that are changed less frequently will function more stably.

## Volatility in the energy industry

Solar energy and wind energy have been described as volatile energy sources in the past, as the amount of energy they supply cannot be predicted with 100 percent certainty. This was and is taken into account when maintaining control power .

## Others

There are financial products whose price is linked to the volatility of an index.

## literature

• Torben Andersen: Volatility Modeling. In: Edward. L. Melnick & Brian. S. Everitt (Ed.): Encyclopedia of Quantitative Risk Analysis and Assessment . Volume 4, John Wiley & Sons, Chichester 2008, ISBN 978-0-470-03549-8 .
• Stefano Bartolini, Peter Mair: Identity, Competition and Electoral Availability. The Stabilization of European Electorates 1885–1985. ECPR Press, Colchester 2007.
• Andreas Ladner: Stability and Change of Parties and Party Systems. A comparative analysis of lines of conflict, parties and party systems in the Swiss cantons. VS Verlag für Sozialwissenschaften, Wiesbaden 2004, ISBN 978-3-8100-4120-3 , (habilitation thesis University of Bern 2002, 488 pages).
• Mogens N. Pedersen: Electoral Volatility in Western Europe. 1948-1977. In: Peter Mair (Ed.): The West European Party System. Oxford University Press, Oxford 1991, pp. 195-208.
• Mogens N. Pedersen: The Dynamics of European Party Systems: Changing Patterns of Electoral Volatility. In: European Journal of Political Research. 7, 1979, pp. 1-26. doi: 10.1111 / j.1475-6765.1979.tb01267.x .
• Wolfgang Rudzio : The political system of the Federal Republic of Germany. 7th updated and expanded edition. VS Verlag für Sozialwissenschaften, Wiesbaden 2006.
• Manfred G. Schmidt : Dictionary of Politics (= Kröner's pocket edition . Volume 404). Kröner, Stuttgart 1995, ISBN 3-520-40401-X .
• Harald Schoen: Voter change and change of election. A comparative study. West German Publishing House, Wiesbaden 2003.
• Rainer-Olaf Schultze: Volatility. In: Rainer-Olaf Schultze, Dieter Nohlen (Hrsg.): Lexicon of political science . Volume 2: NZ. 4th edition. Beck, Munich 2009, ISBN 978-3-406-59234-8 .
• Silvia Willems: France's party system in transition. An analysis of the current party system of the Fifth Republic taking into account institutional, socio-structural and issue-dependent causes of change. Grin-Verlag, Munich 2005.

Wiktionary: volatility  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. ^ Ser-Huang Poon & Clive Granger: Practical Issues in Forecasting Volatility. In: Financial Analysis Journal, vol. 61, 2005, pp. 45-56. JSTOR 4480636
2. Federal Association of German Investment Companies V. (BVI) (1996), circular MR 98/96.
3. ^ John C. Hull: Options, futures and other derivatives. 9th edition. Pearson Education, 2015, ISBN 978-0-13-345631-8 , p. 341.
4. Rainer-Olaf Schultze, Volatility. In: Rainer-Olaf Schultze / Dieter Nohlen (eds.), Lexicon of Political Science, Volume 2: NZ, 2004, p. 1114
5. Manfred G. Schmidt: Dictionary of politics. 1995, p. 1030.
6. ^ Andreas Ladner, Stability and Change of Parties and Party Systems. A comparative analysis of lines of conflict, parties and party systems in the Swiss cantons , 2004, p. 106
7. ^ Mogens N. Pedersen, Electoral Volatility in Western Europe. 1948-1977. In: Peter Mair (Ed.), The West European Party System, 1990, p. 199
8. ^ Andreas Ladner, Stability and Change of Parties and Party Systems. A comparative analysis of lines of conflict, parties and party systems in the Swiss cantons , 2004, p. 99.
9. ^ Andreas Ladner, Stability and Change of Parties and Party Systems. A comparative analysis of lines of conflict, parties and party systems in the Swiss cantons , 2004, p. 99.
10. Stefano Bartolini / Peter Mair, Identity, Competition and Electoral Availability. The Stabilization of European Electorates 1885–1985 , 1990, p. 28
11. Stefano Bartolini / Peter Mair, Identity, Competition and Electoral Availability. The Stabilization of European Electorates 1885-1985 , 1990, p. 28 f.
12. ^ Andreas Ladner, Stability and Change of Parties and Party Systems. A comparative analysis of lines of conflict, parties and party systems in the Swiss cantons , 2004, p. 105 f.
13. ^ Andreas Ladner, Stability and Change of Parties and Party Systems. A comparative analysis of lines of conflict, parties and party systems in the Swiss cantons , 2004, p. 106
14. Rainer-Olaf Schultze, Volatility. In: Rainer-Olaf Schultze / Dieter Nohlen (eds.), Lexicon of Political Science, Volume 2: NZ, 2004, p. 1114.
15. FAZ.net February 7, 2018 / Martin Hock: Explosive potential on the stock exchanges