Hot answers tagged volatility
19
Volatility is mean reverting if the underlying security doesn't drop to zero.
If the security has some underlying "value" then its price is co-integrated with that "value". The volatility is the uncertainty of that price as it tracks the security's "value".
Edit 12/03/2011 =================================================
@pteetor,
I may have missed ...
13
Volatility is typically unobservable, and as such estimated --- for example via the (sample) variance of returns, or more frequently, its square root yielding the standard deviation of returns as a volatility estimate.
There are also countless models for volatility, from old applied models like Garman/Klass to exponential decaying and formal models such as ...
12
One of the reasons the ARCH family of models is used is that you only need price data to generate the model. These data exist back to the 1800s, so ARCH is great for looking at volatility over very long periods. I don't know that I'd say that the ARCH model has a lot of problems -- it solved the problem of not allowing volatility in time or in the level of ...
12
Volatility is mean reverting because you can prove by contradiction that it cannot be otherwise. You have an intuitive understanding of why, but you need something closer to a proof.
Assume volatility is not mean reverting. At time t, the effect of the random component of the volatility on its level will be $\sigma \cdot \sqrt{t}$
For an arbitrarily ...
11
Increased volatility (high VIX) signifies more risk. To keep their portfolio in line with their risk preferences, market participants deleverage. Since long positions outweigh short positions in the market as a whole, deleveraging entails a lot of selling and less buying. The relative increase in selling causes downward pressure on stocks.
11
I've read N. Taleb. Dynamic hedging for exactly the same reason and found it quite helpful. You can find a preview at Google Books to examine the content - the greatest thing about this book that N. Taleb tries to show how things work in pracice not just how to derive another formula (what is a subjsect for other great books on quantitative finance).
10
The price of a binary option, ignoring interest rates, is basically the same as the CDF $\phi(S)$ (or $1-\phi(S)$ ) of the terminal probability distribution. Generally that terminal distribution will be lognormal from the Black-Scholes model, or close to it. Option price is
$$C = e^{-rT} \int_K^\infty \psi(S_T) dS_T$$
for calls and
$$ P = e^{-rT} ...
10
The usual technique of computing the mean and standard deviation of returns happens to coincide with the maximum likelihood estimate when the data are regularly spaced. However, when the data are not regularly spaced, you can still do a maximum likelihood estimate. It's just more computationally intensive than before.
That is to say, assume you have ...
10
I think you are interpreting too much into the matter. The $-\frac12\sigma^2$ is just a correction term that comes from Jensen's inequality.
You need this when switching from supposedly symmetric returns (normal distribution) to the skewed price process (log-normal distribution).
I think there are no deeper truths to be found here.
9
The main underlying difference is in their definition. Variance has a fixed mathematical definition, however volatility does not as such. Volatility is said to be the measure of fluctuations of a process.
Volatility is a subjective term, whereas variance is an objective term i.e. given the data you can definitely find the variance, while you can't find ...
9
By volatility people usually refer to to annualized standard deviation of an asset. For an asset it's usually quoted as a percentage of the asset price (i.e. the return volatility). For a portfolio, it is often quoted in currency units. Variance is the square of the standard deviation. It is usually not quoted directly because it doesn't have an intuitive ...
9
Great question!
I think the most useful starting point is Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options by Bakshi, Kapadia and Madan (2003). Their paper proposes a definition of model-free implied skewness (they originally called it risk-neutral skewness, but MFIS is more accurate), which they prove will ...
8
The optimal growth portfolio is obtained by applying the Kelly criterion which is one of the pillars of the sound risk management.
Ed Thorp's weekend forays to Las Vegas to play blackjack were one of the first historically documented cases of successful practical implementation of the Kelly strategy. Since then this method and its modifications have been ...
8
Technically, yes, the VIX is a measure of implied volatility. But practically speaking, it is a measure of market uncertainty: when market participants are uncertain of the future, they buy options to protect their positions, driving up option premiums and increasing implied volatility.
The broader market hates uncertainty, however, so that same uncertainty ...
8
GARCH(1,1) is a "standard approach for modeling volatility" mainly in academic literature. Most of us in the real world don't use it. Volatility forecasting tends to come more from looking at more-liquid comparables for future market volatility than from fitting fancy retrospective models.
As for ignoring the dependence of residuals, well, folks are ...
8
Implied volatility is the volatility implied by some model. You will have a skew if your model is implying different volatilities for different strikes. However, the realized volatility of the underlying will be the same for all strikes. So, when you are dealing with realized vol, you can drop the "moneyness" axis.
Volatility cones can help you compare ...
8
Some cynical but functional definitions:
It's what you can't model if you're not using tick by tick data
It's what proper quant pricing theory doesn't know how to model yet
It's information (order book behavior) that reflects momentary fluctuations in the supply/demand of a given contract, rather than its underlying value (eg an arbitrage free price)
...
8
Intraday seasonality is a major factor in comparing volatility at different times of day. Most time series display significantly higher volatility in the morning EST than mid-day. For US exchange-traded products, volatility picks up again just before 4:00 PM EST. This is known as the u-shaped volatility pattern for exchange-traded products. A proper ...
8
This is correct: "The general idea of cleansing a correlation matrix via random matrix theory is to compare its eigenvalues to that of a random one to see which parts of it are beyond normal randomness."
This is not correct: "These are then filtered out and one is left with the non-random parts."
The term "filtering", although used extensively in the ...
7
You mention "daily" risk, so I'm assuming you're looking at a daily frequency. Yang-Zhang Volatility (Drift-independent Volatility Estimation Based on High, Low, Open and Close Prices) fits the bill for what you're asking, it takes into account intraday fluctuations as well.
7
If you're mostly trading equities, sell 2-3 month VIX futures, otherwise sell straddles on your non-equity assets or consider the new CME volatility futures on gold, oil, Euro.
chrisaycock isn't wrong: even if your trading system does better during volatile periods, you should be careful not to over-hedge, since losses on your short vol position(s) will ...
7
The paper "Do option markets correctly price the probabilities of movement of the underlying asset? " by Yacine Aït-Sahalia, Yubo Wang, and Francis Yared should in my opinion provide many very usefull elements for this question (look in particular at section 3).
Regards
7
The term has a different meaning to different people.
to econometricians, microstructure noise is a disturbance that makes high frequency estimates of some parameters (e.g. realized volatility) very unstable. Generally this strand of the literature professes agnosticism as to the its origin;
to market microstructure researchers, microstructure noise is a ...
7
There are rigorous econometric definitions, as has already been eluded to by others. For practical purposes, microstructure noise is a component of a price process that exhibits mean reversion on some (possibly time-varying) frequency.
This reversion is particularly attractive to liquidity provisioners, who seek to profit from this noise component (along ...
7
If $X \sim N(\mu, V)$ is multivariate gaussian,
you can write $X = \mu + C Y$
where $ Y \sim N(0,1) $ is a standard Gaussian
and $C$ is the lower-triangular Choleski matrix of $V$.
You can then express
$ v = \sum_{i=1}^n (X_i - S/n)^2 $,
where $ S = \sum_{i=1}^n X_i $,
in terms of $Y$ and $C$.
(I do not reproduce the computations: they are straightforward.)
...
7
The way market makers mark their volatility curves is by using models which 'fill in the gaps', i.e. they will make a price for a given option even if they do not believe this option is going to get a lot of volume. They are still willing to go long/short because they have a strategy to hedge their overall position (i.e. by managing their greeks and ...
7
The key to this is to think about the enterprise value of a business separately from how it is financed.
For simplicity sake, consider a business that comprises a sole gold bar (no workers, no extraction costs, etc). The value of the business is clearly just the value of the gold bar. If it were a listed company, with no debt, then the equity ...
6
Q1 - Yes, debt load has an impact on the stock price. For instance, say you are valuing a company with a discounted cash flow model, while the interest won't affect the operational cash flows, it will increase the cost of capital. With that, the perceived value will be less than a similar company with less debt. Debt will also affect the volatility of the ...
6
VIX is mechanically determined from the price of S&P500 call and put options. So if the demands for S&P500 calls/puts rise, then the prices rise, then the implied vol from these options rises. During a down market there's a lot of demand for portfolio protection. If you're diversified, then S&P500 puts are good protection, so the prices for puts ...
6
Var and vol swaps are very similar products, with the leverage (convexity) being the biggest theoretical difference, yes.
In the actual market however they are very different. After the 2008 debacle var swaps in the single stock space are not too common, whereas single stock vol swaps are regularly quoted. One interesting perspective is trading one versus ...
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