# Questions tagged [variance]

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9 questions
1answer
1k views

### Variance replication using options

I would like to understand the intuition behind the following question: Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying? A variance swap ...
1answer
12k views

### How to calculate the conditional variance of a time series?

I am reading a paper where the term conditional variance is mentioned, but I am not really sure what is meant by this and how this can be calculated: Fig. 2 shows the conditional variances of the ...
11answers
5k views

### 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 ...
8answers
50k 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?
2answers
542 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 ...
3answers
3k views

### Variance of time integral of squared Brownian motion

I want to calculate the variance of $$I = \int_0^t W_s^2 ds$$ I was thinking I could define the function $f(t,W_t) = tW_t^2$ and then apply Ito's lemma so I get f(t,W_t)-f(0,0) = \int_0^t \frac{\...
1answer
251 views

### 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 ...
1answer
715 views

### Calculating Variance Explained from PCA Loadings

I have a return history for a universe of risky assets and I've run a principal component algorithm and obtained a loadings matrix (num_factors by num_assets) for the first 5 factors. I have a ...
1answer
144 views

### Risk, required return and expected volatility - what is the relationship?

Return required from risk averse agents from risky investments are proportional to expected return variance. That is from the textbook, you take the portfolio with the highest return to standard ...