# 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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### How is Itô's Lemma connected to Messmore's Variance Drain?

How does Itô's Lemma explain the concept of volatility drain in investment returns, and how do the associated equations illustrate this effect? I did the following considerations so far: In financial ...
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### Heston model: odd simulations of variance and asset price process path

I've done Monte Carlo simulations of asset and variance processes of the Heston model on Silver via a Full Truncation of Euler discretisation scheme to learn and see for myself how the simulation ...
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### How the variance process in discretised form influence the asset price in the Heston model

I'm trying to do Monte Carlo simulation paths of an asset price with time step $\Delta t$ via the discretised Euler scheme. My main question is how does the variance process influence the asset price ...
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### How to calculate realized variance?

I have data about all order book events for a day. I know the midpoint price for each time when something happened to the LOB. If I use all of this data to calculate, I get a high daily realized ...
1 vote
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### Emanuel Derman Volatility Approximation [closed]

Can someone please explain Emanuel Derman's volatility approximation as given below? Under Linear Skew If skew is assumed to be linear, at least for strikes relatively close to the money, then Derman’...
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### Predictive Forecast (Close, 14)

I've been following an asset wherein a "R-squared predictive forecast (close, 14)" is posted online each day. On some days, this figure is extremely high, like .92. Exactly what is the ...
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### How to prove the inequality for the standard deviation of a linear combination of two random variables

The variance of the linear combination V of random variables X₁ and X₂ is given by the following formula: $$\sigma_{V}^{2} = s^{2} \sigma_{1}^{2}+(1-s)^2 \sigma_{2}^{2}+2 s(1-s) c_{12}$$ where s and ...
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### Variance decomposition in the frequency domain

I have done a time-domain decomposition of a generalized forecast error variance from a VAR model of exchange rates and inflation rates. The data are monthly. I am not very adept at doing the ...
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### How to calculate historical returns and variance for a non-BAH trading strategy?

Suppose i have a strategy that is not buy-and-hold type of strategy. It can have unique entry timing and unique exit timing for a single asset and both long and short positions will be allowed, and ...
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### Cross corridor var swap

How should I think about replicating a cross corridor variance swap like breaking into strips of calls and puts and an over hedge that I can rebalance at some frequency? Given the earnings move, I can ...
1 vote
113 views

### How to calculate the spot variance from the TSRV (Two-Scale Realized variance)

If the TSRV is given by: $$TSRV = \frac{1}{K} \sum_{i=K}^{n} (S_i - S_{i-K})^2 - \frac{\bar{n}}{n}\sum_{i=1}^n (S_i - S_{i-1})^2$$ where $\bar{n} = \frac{n - K + 1}{K}$, with $n$ is the number of ...
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### Standard deviation of large equal-weighted portfolios

Say I've got a portfolio of shares with the following parameters: Let $n$ be the number of shares in the portfolio, let $\bar\sigma$ be the average standard deviation (volatility/risk) for each share, ...
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### JDOI variance reduction method python

Has anyone read the paper 'JDOI variance reduction method and the pricing of American-style options' by Johan. I want to implement the simulation. But For Monte carlo I got different results. andI ...
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### Multiplicative Metric Variance

I come from a math/statistics background and as learned some stuff as a data analyst I learned a certain technique to calculate period to period variances between some metrics. I was wondering if ...
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### CBOE dispersion index formula

I came across the CBOE white paper Cboe S&P 500 Dispersion Index Methodology. The formula in Subsection Index Construction/Outline of the Dispersion Index Methodology on page 4 that defines the ...
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### Forecasting Realized Volatility with Machine Learning [closed]

How is the daily realized variance calculated for an intraday one minute data. How can realized volatility be forecasted using machine learning techniques such as neural network and LSTM. Any detailed ...
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### negative portfolio variance? Creating a positive semi definite matrix in excel

I am attempting a portfolio optimization model and ended up generating negative portfolio variance using 2WaWbσaσbcorrel(a,b) or 2WaWb*Cov(a,b) From reading the linked article where other users had an ...
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### Is there any relationship between the Covariance(A, B) and the variance of the synthetic asset A/B?

Let's say we have 2 pairs of currencies: EUR/USD and GBP/USD. The cross-asset (or synthetic asset) would be (EUR/USD) / (GBP/USD) = EUR/GBP. Is there any relationship between the covariance(EUR/USD, ...
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### Why do we need the covariance when calculating portfolio VaR?

I was recently learning about value at risk and how to calculate it, and one of the steps was to calculate the covariance of the returns of the securities making up the portofolio. This makes sense ...
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1 vote
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### Why is $Z_t$ uncorrelated with $X_{t-1}$ in $X_t=\theta X_{t-1}+Z_t$?

In a solution to the problem below, the teaching assistant solves it by calculating $\mathbb{E}[X_t^2]$ and ends up with also having to calculate $\mathbb{E}[X_{t-1}Z_t]$ after expanding the square. ...
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The Variance Risk Premium (VRP) is defined as: $$VRP(t,t+\Delta t) \equiv RV(t,t+\Delta t)^2 - IV_t(t,t+\Delta t)^2$$ where $RV^2$ is the realized variance between $t$ and $t + \Delta t$ and $IV_t^2$ ...