# 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".

### Square root

**square rootssquareradical**

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.