# Questions tagged [variance]

Used for questions related to statistical measure "variance", i.e. a second central moment of a random variable. The variance is a risk measure.

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### Lévy alpha-stable distribution and modelling of stock prices.

Since Mandelbrot, Fama and others have performed seminal work on the topic, it has been suspected that stock price fluctuations can be more appropriately modeled using Lévy alpha-stable distrbutions ...
56k views

### What is the difference between volatility and variance?

How do volatility and variance differ in finance and what do both imply about the movement of an underlying?
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### Why would an investor trade a variance swap over a volatility swap?

Why would an investor trade a variance swap over a volatility swap? Is it simply related to the leverage involved in a Var (i.e. sigma-squared) or is there something else to it?
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### Approximately what proportion of a stock’s volatility is explained by market movement?

Assume we decompose the daily (log) returns of a stock as beta times market movement plus an idiosyncratic part. If this is done ex-ante, what proportion of the variance is explained by the market ...
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### Derivation of VIX Formula

I've read a lot of derivations about VIX formula. I can say it is -adjusted- fair strike of variance swap. But I can't see how it goes from variance swap rate to VIX formula. In particular I can't see ...
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### Why is a variance swap long skew?

I can appreciate the mathematical derivation, but can anyone explain this in a more intuitive sense? I often come across the mistaken belief that due to the replicating portfolio being long more ...
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### Do weights from portfolio theory contain bias?

I want to experiment with some portfolio modelling and I was wondering if you guys could help me with something. If I try to estimate and implement the traditional two-fund portfolio consisting of one ...
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### Variance swap replication and variance vega

Noob here. I've been trying to gain a better understanding of variance swaps and what better way than to replicate it with a portfolio of better understood instruments. I have read the GS 1999 ...
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### Jim Gatheral's assertion on ATM implied volatility vs. square root variance

In Jim Gatheral's book The Volatility Surface Section Dependence on Skew and Curvature on page 138, he asserts that We know that the implied volatility of an at-the-money forward option in the ...
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### Conditional or unconditional volatility?

I am reading a paper (reference below) that states "The conditional volatility for each underlying security (or for a market index) can be estimated using the standard deviation of the stock’s ...
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### CAPM model as a regression

The CAPM model states that the returns of a stock are- $r_s=r_f+\beta (r_m-r_f)+\varepsilon_s$ The $\beta$ defined above is then calculated as $\frac{cov(r_s,r_m)}{var(r_m)}$. My question is ...
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### What are the significant implications of the long-run average variance rate and why Engle won the Nobel Prize for ARCH model development?

In a ARCH(m) model we have $$\sigma_n^2=\sum_{i=1}^{m} \alpha_i u_{n-i}^2$$ where $u_i$ is defined as the continuously compounded return during day $i$ (between the end of day $i-1$ and the end of ...
567 views

### Choice of prior as a shrinkage target in portfolio construction?

There's various research showing how priors such as the minimum variance portfolio turn out to be a surprisingly effective shrinkage target in portfolio construction. The sell point of these priors ...
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### Static and Dynamic Hedging of Vol/Var Swaps

Why can a variance swap be perfectly statically hedged whereas a volatility swap requires dynamic hedging? Possible reference request to the corresponding literature.
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### How to scale option pricing components in regard to time

I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model. I have run into a very basic question. How should I scale the input variables in regard to time? My ...
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### What is the difference between squared returns and variance?

I am trying to calculate 1-day ahead volatility forecasts using the exponentially weighted moving average, however I am unsure on how to read the formula provided within Risk-Metrics Technical ...
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### How to estimate the variance of this stochastic process?

I have an unobservable stochastic quantity $\lambda(t)$, which I analytically know the variance of, that is $$\text{Var}(\lambda(t))= \frac{\theta \sigma^2}{2\kappa}$$ My goal is to get an estimate ...
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### Why are there different estimators for stock volatility? (realized variance, RAV, etc)

I am very confused about why different volatility estimators (RV, RAV, BPV, etc) exist. If the goal is to find the best estimator for stock volatility, and volatility is latent, how do I know which ...
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### How to Compute the payoff of Var Swaps, which I have replicated

I used Derman(1999) method, to calculate the fixed Kvar for Variance Swaps using actual option price data. The first Pic Shows the outcome. (ignore the 0s). Now the profit and loss of short var swaps ...
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### Usages of variance swap

I’m interested in variance swap. Considered from its feature, variance swap is used for betting the (historical) volatility of underlying asset. If we use it for hedge tool of Vega or Volga, does it ...
As far as I understand, Variance Swap (VS for short) function as follows : no payment when entering the contract at maturity the VS buyer pays a strike $K^2$ and is paid (by the VS seller) the ...