# Volatility (finance)

volatilityvolatileprice volatilityprice fluctuationmarket volatilityvolatility structurechangefinancial market volatilityfluctuated wildlyfluctuates
In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.wikipedia
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### Implied volatility

implied volatilitiesimplied volvolatilities implied
Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option).
In financial mathematics, the implied volatility of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes) will return a theoretical value equal to the current market price of the option.

### Standard deviation

standard deviationssample standard deviationsigma
In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.
The standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment.

### Finance

financialfinancesfiscal
In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.
(Other risk types include foreign exchange, shape, volatility, sector, liquidity, inflation risks, etc.) It focuses on when and how to hedge using financial instruments; in this sense it overlaps with financial engineering.

### Realized variance

Realized Volatility
near synonymous is realized volatility, the square root of the realized variance, in turn calculated using the sum of squared returns divided by the number of observations.
The realized volatility is the square root of the realized variance, or the square root of the RV multiplied by a suitable constant to bring the measure of volatility to an annualized scale.

### Rate of return

returnreturnsreturn on investment
In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.
The difference between the annualized return and average annual return increases with the variance of the returns – the more volatile the performance, the greater the difference.

### Variance swap

In today's markets, it is also possible to trade volatility directly, through the use of derivative securities such as options and variance swaps.
A variance swap is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock index.

### Option (finance)

optionsoptionstock options
actual future volatility which refers to the volatility of a financial instrument over a specified period starting at the current time and ending at a future date (normally the expiry date of an option) 8) Volatility affects pricing of options, being a parameter of the Black–Scholes model.
an estimate of the future volatility of the underlying security's price over the life of the option.

### Local volatility

Although the Black Scholes equation assumes predictable constant volatility, this is not observed in real markets, and amongst the models are Emanuel Derman and Iraj Kani's and Bruno Dupire's local volatility, Poisson process where volatility jumps to new levels with a predictable frequency, and the increasingly popular Heston model of stochastic volatility.
A local volatility model, in mathematical finance and financial engineering, is one that treats volatility as a function of both the current asset level S_t and of time t. As such, a local volatility model is a generalisation of the Black-Scholes model, where the volatility is a constant (i.e. a trivial function of S_t and t).

### Volatility arbitrage

See Volatility arbitrage.
The objective is to take advantage of differences between the implied volatility of the option, and a forecast of future realized volatility of the option's underlying.

### Black–Scholes model

Black–ScholesBlack-ScholesBlack–Scholes formula
Although the Black Scholes equation assumes predictable constant volatility, this is not observed in real markets, and amongst the models are Emanuel Derman and Iraj Kani's and Bruno Dupire's local volatility, Poisson process where volatility jumps to new levels with a predictable frequency, and the increasingly popular Heston model of stochastic volatility. 8) Volatility affects pricing of options, being a parameter of the Black–Scholes model.
\sigma is the volatility of returns of the underlying asset

### Stochastic volatility

random volatilitystochasticallyVolatility
Although the Black Scholes equation assumes predictable constant volatility, this is not observed in real markets, and amongst the models are Emanuel Derman and Iraj Kani's and Bruno Dupire's local volatility, Poisson process where volatility jumps to new levels with a predictable frequency, and the increasingly popular Heston model of stochastic volatility.
The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others.

### Volatility tax

Volatility thus mathematically represents a drag on the CAGR (formalized as the "volatility tax").
The volatility tax is a mathematical finance term, formalized by hedge fund manager Mark Spitznagel, describing the effect of large investment losses (or volatility) on compound returns.

### Autoregressive conditional heteroskedasticity

ARCHARCH modelGARCH
This is termed autoregressive conditional heteroskedasticity.
ARCH models are commonly employed in modeling financial time series that exhibit time-varying volatility and volatility clustering, i.e. periods of swings interspersed with periods of relative calm.

### Beta (finance)

betabeta coefficient beta coefficient
Beta (finance)
A beta below 1 can indicate either an investment with lower volatility than the market, or a volatile investment whose price movements are not highly correlated with the market.

### IVX

IVX
IVX is a volatility index providing an intraday, VIX-like measure for any of US securities and exchange traded instruments.

### Emanuel Derman

DermanDerman, EmanuelMy Life as a Quant
Although the Black Scholes equation assumes predictable constant volatility, this is not observed in real markets, and amongst the models are Emanuel Derman and Iraj Kani's and Bruno Dupire's local volatility, Poisson process where volatility jumps to new levels with a predictable frequency, and the increasingly popular Heston model of stochastic volatility.
He is the author of numerous articles on quantitative finance on the topics of volatility and the nature of financial modeling.

### VIX

CBOE Volatility Index (VIX)Fear IndexS&P 500 VIX Futures Index
VIX
The CBOE Volatility Index, known by its ticker symbol VIX, is a popular measure of the stock market's expectation of volatility implied by S&P 500 index options.

### Volatility smile

volatility surfacevolatility skewImplied volatility surface
Volatility smile
Volatility (finance)

### List of things named after Carl Friedrich Gauss

gaussianCarl Friedrich GaussGaussian modeling
For a financial instrument whose price follows a Gaussian random walk, or Wiener process, the width of the distribution increases as time increases.

### Random walk

random walkssimple random walkrandom walker
For a financial instrument whose price follows a Gaussian random walk, or Wiener process, the width of the distribution increases as time increases.

### Wiener process

Brownian motionstandard Brownian motion(Wiener) process
For a financial instrument whose price follows a Gaussian random walk, or Wiener process, the width of the distribution increases as time increases.

### Probability

probabilisticprobabilitieschance
This is because there is an increasing probability that the instrument's price will be farther away from the initial price as time increases.

### Lévy distribution

LévyLévy stable distributionslog-Levy distributions
Since observed price changes do not follow Gaussian distributions, others such as the Lévy distribution are often used.

### Fat-tailed distribution

fat tailfat tailsfatter tails
These can capture attributes such as "fat tails".