Serving the Quantitative Finance Community

 
User avatar
Paul
Topic Author
Posts: 6604
Joined: July 20th, 2001, 3:28 pm

What is volatility?

February 2nd, 2006, 2:41 pm

I am sure ITO33 will like to hear answers to this one!P
Last edited by Paul on February 2nd, 2006, 11:00 pm, edited 1 time in total.
 
User avatar
damel
Posts: 3
Joined: January 8th, 2006, 12:02 pm

What is volatility?

February 2nd, 2006, 2:53 pm

A statistical measure of the tendency of a market or security to rise or fall sharply within a period of time.Volatility is typically calculated by using variance or annualized standard deviation of the price or return. A measure of the relative volatility of a stock to the market is its beta. A highly volatile market means that prices have huge swings in very short periods of time.I take these standard definitions from http://www.investopedia.com/terms/v/vol ... Volatility has a huge use in finance and at a basic level is a proxy for the riskiness of an asset.
 
User avatar
Fermion
Posts: 2
Joined: November 14th, 2002, 8:50 pm

What is volatility?

February 2nd, 2006, 11:13 pm

Empirically, I would say it is usually taken to mean the standard deviation over a given time interval. But attempts to express that more precisely usually introduce other model-dependent ideas (e.g. dividing by the square root of the time interval).The problem as I see it lies in a fundamental ambiguity in trying to separate a smooth drift from random fluctuations. This is problematic because it entails trying to separate one number into two -- which cannot be done uniquely without imposing further constraints. (E.g. take the first difference of a single time step. Was it due to a smooth drift or a fluctuation?)As a consequence we can define volatility in numerous ways, each by imposing a constraint which in reality constitutes a model. For example, we can define it as the amplitude of a Wiener process, assume constancy over several time steps and then average it. Or we can modify a Wiener process to allow the amplitude to vary, perhaps deterministically or perhaps stochastically. Even if the real process is not a Wiener process, then we can still use such definitions to extract numbers which may be useful.IMHO this inherent ambiguity is too often glossed over in finance theory (often because of the need to provide traders with something simple to work with in the heat of the trading floor). This can result in the real underlying process being obscured by primitive models.
 
User avatar
msankowski

What is volatility?

February 14th, 2006, 8:39 pm

Volatility is the measure of how much a price of an asset has changed over time. Usually, volatility is indicated by a summary statistic of some sort, like a moving average or a standard deviation, because we assume that many observations give more information than one observation. The most common measure of volatility is the standard deviation of the closing prices over a year. When you read an asset has a volatility of 16%, it means that the standard deviation of the prices in the last year was 16%. There are many other ways to calculate the volatility of an asset, but the central concept is that volatility is the amount of change in the price of the asset over a period of time. Here are the names of some other methods of calculating and measuring volatility:Garman-KlassParkinsonAverage True RangeBetaVolatility is the most common measure of risk in trading. We make a differentiation between historical and implied volatility. Historical volatility is calculated from historical prices or information, as explained above.Implied volatility is calculated as the output of an options pricing model. In a standard options pricing model, you need a volatility to calculate the price of an option. If you know this volatility, you can calculate a price. However, you are holding the option over a period of future time, and therefore the volatility of the asset is not known. As a result, traders make guesses about the future volatility of this asset, some better than others. This market creates a price for the option, and with that price, you can then calculate the volatility associated with that option price. This is known as the implied volatility.
 
User avatar
bogaso
Posts: 1
Joined: March 3rd, 2008, 7:21 am

What is volatility?

March 4th, 2008, 4:21 am

I would like to ask what is conditional volatility and what is unconditional volatility.
 
User avatar
exotiq
Posts: 2
Joined: October 13th, 2003, 3:45 pm

What is volatility?

April 16th, 2008, 1:04 pm

As it says, "conditional volatility" is a measure of how much a financial variable moves where only data points of these movements subject to some condition are counted (the others are ignored). There are at least two relatively common types of conditional volatility:1. "Semi-variance" - this is a way of measuring volatility by counting say, only up moves (positive returns) or only down moves (negative returns). The idea is to capture whether down moves tend to be greater in magnitude on average than up moves, as well as to isolate volatility as a measure of risk / risk aversion (since many investors care more about "downside" volatility than "upside" volatility. Over finite time horizons, "skew" (as it appears in many equity indices) basically means that up moves are more likely than down moves and that down moves tend to be larger than the up moves (keeping the expectation where it is).2. "Corridor / Range" variance - this is a measure of volatility where moves are only measured if the financial variable is in a certain range (for example, count the volatility of all returns when SPX > 1,400 and ignore all other data points). "Corridor variance swaps" have become a commonly traded OTC derivative, probably in no small part due to the fact that they price in skew in a view similar to how local and stochastic vol models look at skew (in the case of many equity indices, vol tends to be lower as the level of the index is higher and vice versa).Note that in the Black-Scholes style drift+diffusion framework, the local infinitesimal step is always normally distributed, and it is the fact that volatility changes over time (for different values of the financial variable) that creates skewed distributions over finite time frames.Hope this helps...
 
User avatar
talkingheads
Posts: 0
Joined: April 12th, 2008, 3:14 pm

What is volatility?

June 11th, 2008, 3:24 pm

i have some questions about volatility:1. estimating volatility as std of closing prices versus std of logreturn versus std of daily return; which one is a better proxy of volatility?2. what can you do when volatility changes? (i mean that if you take last 250 observations and estimate volatility, it will be different from volatility i estimated a month ago with 250 observations i had than)thanks