# 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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117 views

### Empirical equivalent for implied vol

Implied volatility is supposed to show volatility of the underlying over next k days where k - maturity of the option. Say our stock price is $S_t$ and percentage return is $r_t$. Then which empirical ...
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### GARCH(1,1) variance forecast in one-step or multi-step?

Suppose I want to forecast daily variance of a stock using GARCH(1,1) model while I have high frequency data of 5 minute returns. What is the difference between applying GARCH(1,1) in one-step ...
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### Someone help me understand why for portfolio variance or Parametric Value at Risk we have to compute the covariance matrix?

I understand that portfolio variance is computed through $w'Cw$, where w is the vector of weights, $C$ being the covariance matrix. However, what I don't get is this: why can't this portfolio variance ...
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### How to reduce variance in Monte Carlo using Control Variates when spot prices are decreasing?

I'm trying to use the Control Variates technique to reduce the variance of the estimate obtained from a Monte Carlo simulation for option pricing. As suggested in the book by Glasserman I'm using this ...
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### Change in variance time series

I am analysing a time series (stock returns) and I am trying to check whether variance in the second half of my sample is different from the first half. I assigned a period to the observations. Here ...
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### Minimal bounds to enclose most sample paths of a GBM (Geometric Brownian Motion)

For a (generalized) Brownian motion $Y = F(t,W)$, starting at $InitialValue$ and running for a total of $T$ time, if I want to "enclose" (in a visual way) "most" of the possible sample paths, I could ...
104 views

### Variance risk premium: When is realized vol higher than implied vol in practice?

I’m doing some work around the variance risk premium currently, and I’m interested in understanding the situations when realized volatility is > implied volatility in practice. I know in generally ...
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### Hedging vega risk with varswaps

I have encountered a statement that in summary reads like this: Varswaps became popular after the LTCM meltdown due to high levels of implied volatility the market was seeing at the time. Hedge funds ...
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### CBOE Skew Index Intuition

I was recently reading (and very much struggling to understand) the CBOE white paper on their Skew Index (CBOE Link), I thought it might be useful as I'm trying to better understand volatility skews. ...
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### Deriving the VIX formula

I am having trouble filling in a few steps in the derivation. From Martin (2017), we get the following assumptions: Constant continuously compounded rate $r$; The underlying doesn't pay dividens; ...
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### Calculating covariance from three variances

I have been asked to look to refactor some code. There is a line shown below: $\text{implied covariance} = -\frac{(\text{var}_1 - \text{var}_2 - \text{var}_3)} {2}$, where $\text{var}_1$ is the ...
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### Variance/VaR calculation for a Portfolio

I'm considering a portfolio of multiple stocks (>2), and calculating their Standard Deviation/Variance and VaR for the portfolio. My question is about the below two ways to calculating them Consider ...
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### What is the difference between standard deviation, volatility and quadratic variation?

What is the difference between standard deviation, volatility and quadratic variation? As I know, volatility is the standard deviation of the log returns, so they are basically the same. (One of ...
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### Expected value and variance of the stock log-returns under Local Volatility framework

I want to calculate the expected value and the variance of the stock process log-returns in the Local Volatility setting (and the realized/terminal correlation but let us begin in the one-dimentional ...
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### Uncovering patterns in price timeseries using linear regression

I have some minute-bar data which my professor suggested I resample to 5 minute bars and then separate it into timeseries per bar period. For example, I get one time series for 12:00, another one for ...
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### Options on realized volatility / variance

If I'd like to price options on variance/volatility in the Heston model. Is MC simulation and/or finite difference the only way to do it? Or is there an analytical expression for the probability ...
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### Mean-Variance portfolio: How do I compute the variance when the portfolio is normalized

Let's consider the very basic of a Mean-Variance Portfolio: $$\text{max}_{x} (1-\lambda)\sum_i^n\mu_ix_i-\lambda\sum_i^n\sum_j^n x_i Q_{ij}x_j$$ \text{ s.t. }\sum_i^nx_i=1 \text{ , } x_i \geq ...
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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 ...
Suppose that the stationary series $r_t$ is well fitted by an $ARMA(p,q)+c$ and $GARCH(r,s)$ model, where $GARCH(r,s) = \sigma_t ^2$ If in the testing sample I have to graphically compare the ...