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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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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’...
toobigtofail's user avatar
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1 answer
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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 ...
Chris's user avatar
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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 ...
bokabokaboka's user avatar
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33 views

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 ...
Pavel Filip's user avatar
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13 views

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 ...
Kevin Kim's user avatar
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64 views

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 ...
exotics101's user avatar
1 vote
1 answer
80 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 ...
Xerium's user avatar
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1 answer
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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, ...
j3141592653589793238's user avatar
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11 views

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 ...
Elmy Zhang's user avatar
1 vote
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60 views

Margin period of risk and scaling (MPoR)

I'm analyzing the formula to approximate the Margin Period of Risk (MPoR) for linearly linearly decreasing to zero exposure. Given the MPoR at $\tau$ one can evaluate the continious total exposure at $...
bag_dush's user avatar
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Approximation of an Itô integral with python

Exercise 3.11 (Approximation of an Itô Integral). In this example, the stochastic integral $\int^t_0tW(t)dW(t)$ is considered. The expected value of the integral and the expected value of the square ...
Jessie's user avatar
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1 answer
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Problem with finding the efficient capital market line formula, getting negative variance

So my goal is to write the Capital Market line formula considering this data: $\[ \begin{array}{|c|c|c|} \hline \text{Stock 1} & \text{Stock 2} & \text{Probability} \\ \hline -15\% &...
Google Account's user avatar
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2 answers
132 views

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 ...
hyg17's user avatar
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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 ...
Hans's user avatar
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1 vote
1 answer
118 views

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 ...
Samuel Gyamerah's user avatar
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81 views

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 ...
user14894283's user avatar
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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, ...
Hiperfly's user avatar
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2 answers
234 views

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 ...
abdelrahman esmat's user avatar
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1 answer
175 views

Covariance Matrix of Correlated Random Variable

Suppose I know or have estimated the covariance matrix for one random variable (for example an asset) and have: $$ \begin{bmatrix} <\text{spot, spot}> & <\text{atmv, spot}> \\ <\...
roz's user avatar
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Single outsized daily return value creates substantive discrepancy between annualized variance calculated from daily vs monthly returns

I am new here, and to the field. I hope my clunkiness in expressing myself can be forgiven. My situation is as follows: I have around three years of daily return data for some financial asset. Out of ...
Tim Molendijk's user avatar
2 votes
0 answers
128 views

Standard Deviation and Monotonicity property

I just read that standard deviation is a coherent risk measure, and therefore it should satisfy the monotonicity property: $X_1 \geq X_2 \implies \rho(X_1) \leq \rho(X_2)$ where $X_1,X_2$ are asset ...
Andrei's user avatar
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Bessel Correction and Geometric Brownian Motion

Does it make sense to use bessel's correction for standard deviation and variance when fitting the drift and volatility parameters of geometric brownian motion to historical return data for a security....
user3163829's user avatar
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1 answer
341 views

constant dollar Gamma for variance swap

Here is the result of Gamma for Variance swap. I think $S_t$ is the only variable in $\sigma^2_{Exected,t}.$ Then how could we get the presentation of Gamma: $$\dfrac{1}{S_t^2},$$ there should be some ...
user6703592's user avatar
2 votes
0 answers
108 views

Does the expected return increase with variance for stocks? [duplicate]

I took a historical dataset of ~2600 stocks and computed the 30-day returns for non-overlapping windows, for a 9 year period. For the returns, I computed the mean and variance. Then I plotted the mean ...
Botond's user avatar
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2 answers
430 views

What is the Fair Strike in a Var/Vol Swap and how does it relate to its price? [closed]

I am a student trying to price volatility and variance swaps. People who price those two products usually try to get the "fair strike", and don't seem to care about the price. However, I ...
Ozee's user avatar
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1 answer
257 views

How to derive numeric option VaR with delta-vega normal approach?

For an option with price C, the ΔC, with respect to changes of the underlying asset price S and volatility σ (first-order approximation), is given by $\Delta C=\delta \Delta S+\nu\Delta\sigma$, where ...
userLx's user avatar
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Bias-Variance tradeoff for Covariance Estimation w/ Different Frequencies

In general, what does the bias-variance tradeoff look like when estimating covariance matrices with varying return frequencies (i.e. daily, weekly, monthly returns)? From my observations I've noticed ...
Ringleader's user avatar
1 vote
1 answer
590 views

Calculating variance of long/short portfolio

Say I have a portfolio of stocks, stock A, stock B and stock C, with the below positions: stock A: long 100 USD stock B: long 50 USD stock C: short 200 USD How do I calculate the portfolio variance ...
Harry's user avatar
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1 answer
280 views

Smile wings and varswap pricing

Is it true that far wings of the volatility smile have an outsized influence on the price of a variance swap? Is there a mathematical argument demonstrating this idea? What do we generally refer as ...
fwd_T's user avatar
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3 votes
1 answer
121 views

Compute monthly realized variance for Fama-French factor

I need to compute monthly realized variance from daily data for Fama-French factors. Knowing that Fama-French factors is the difference of return between different type of stocks, for example SMB ...
Neda Fathi's user avatar
1 vote
0 answers
118 views

Minimizing variance of a long short equity portfolio in practice

I understand the finance 101 explanation of how to minimize variance of a long-short portfolio using a covariance matrix. I also know that it doesn't really work because the covariance matrix is ...
helloimgeorgia's user avatar
1 vote
0 answers
73 views

Calculating monthly UST3M returns

I am trying compute a variance/covariance matrix for 5 stocks using monthly returns. I plan to use CAPM (using monthly log returns) as the expected return and the US 3-month Treasury Bill (UST3M) ...
Tony STRATAN's user avatar
1 vote
1 answer
517 views

Compute monthly realized variance from daily data

I am confused about the correct formula to compute monthly realized variance from daily data. What is the first sigma in the picture: sum or average? I mean, after subtracting each observation from ...
Neda Fathi's user avatar
2 votes
1 answer
612 views

How does autocorrelation bias annualizing variance?

I read somewhere that autocorrelation prevents someone from annualizing variance. But how does it bias it? Let's say you have daily returns. If autocorrelation is high, should that overstate or ...
confused's user avatar
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2 votes
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133 views

How is the variance schedule used?

Let $v(t)$ be the instantaneous variance of an underlying stock or index at time $t\in[0,1]$ between the open at $t=0$ and close at $t=1$ of an exchange. Usually $v(t)$ achieves local maxima at $t\in\{...
Hans's user avatar
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-1 votes
1 answer
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Daily vs Monthly vs. other return for volatility calculation?

I thought I read/heard somewhere that annualized volatility, using monthly returns vs daily returns is usually lower. With that said, I can't seem to find any papers on this. Does anyone have any ...
confused's user avatar
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2 votes
0 answers
132 views

Best way to extrapolate on implied volatility

I am doing some standard svd calibration to mark market implied vols in difference to a previous volatility surface. For longer term maturities where there is no market data, I am extrapolating ATM ...
Victor Gl's user avatar
2 votes
1 answer
192 views

Deriving the variance of G2++ Model

I'm studying G2++ Model in Brigo(2007)'s book. The model constructed as follows, $$ r(t) = x(t) + y(t) + φ(t), \quad r(0) = r_0\\ $$ with the dynamics of $dx(t)$ and $dy(t)$ described by: \begin{align}...
user13232877's user avatar
1 vote
0 answers
80 views

How much compensation need to take on risk?

Quant Firm Interview Question We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase ...
MrChair549's user avatar
1 vote
1 answer
325 views

Variance of the price from returns variance

Let's say that we have the variance of the daily return at $t_0$: $$\sigma_{r_{t_0}}^2=\text{Var}[r_{t_0}]=\text{Var}[\frac{S_{t_0}-S_{t_0-1}}{S_{t_0-1}}]$$ for price process $S_t$. Is there a way to ...
Michał Dąbrowski's user avatar
0 votes
1 answer
93 views

Verify numerically relation between mean deviation and standard deviation

I was reading "We Don’t Quite Know What We Are Talking About When We Talk About Volatility" by Goldstein and Taleb, and I was trying to quickly verify numerically the relation between mean ...
EC_crypto's user avatar
3 votes
2 answers
527 views

Kelly Criterion — maximize expected value and minimize the variance in card game with $x$ red and $y$ black cards

You have $x$ red cards and $y$ black cards. I flip them over one at a time. The probability of flipping a particular colour is proportional to the amount of those coloured cards left. You start with $...
Mining's user avatar
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0 votes
1 answer
81 views

Variation of the trading range

Example: The trading range (in points) for each of the last 5 trading days for asset A is: 5,21,2,15,32 and for asset B is: 5,6,5,5,5. Is there an indicator that ranks assets based on variation of ...
user avatar
0 votes
1 answer
620 views

Control Variates - Option pricing

I am trying to reduce the Monte Carlo variance with Control Variates technique. In practice, I am able to reduce it with a generic European Call option, with the following formulas: $$ Z_{CV} = \frac{...
John_maddon's user avatar
1 vote
1 answer
192 views

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. ...
Parseval's user avatar
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1 vote
0 answers
216 views

Computing the Variance Risk Premium

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 $IV_t^2$ ...
Jordan Wrong's user avatar
6 votes
2 answers
576 views

Heston: Variance of Integrated Variance

Consider the standard Heston model\begin{align*} dX&=\left(r-\frac{1}{2}v\right)dt+\sqrt{v}dB,\\ dv&=\kappa(\theta-v)dt+\xi\sqrt{v}dW, \\ dBdW&=\rho dt. \end{align*} Computing $\mathbb{E}\...
Alex's user avatar
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0 answers
208 views

Monte Carlo Simulation of GBM Process has a Very High Variance - Explanation Needed as to why?

I use Geometric Brownian Motion (GMB) to simulate a share price from March 24, 2020 to March 24 as follow: \begin{equation} S_t=S_{t-1}exp((rf-0.6\sigma^2)*(2)+\sigma*sqrt(2)*\mathcal{N}(0,1)) \end{...
nemiii's user avatar
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3 votes
1 answer
261 views

Market-maker's gain variance

I am reading the book "Trades, Quotes and Prices" by JEAN-PHILIPPE BOUCHAUD and have stuck in the very beginning with understanding the formula of variance of MM's gain per trade (see ...
Artemy's user avatar
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0 votes
1 answer
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Show that the following result holds true for the variance of the return of a portfolio of shares

Start with a portfolio $p$ of $n$ shares, each with weight $x_i = \dfrac{1}{n}$ (for $i$ ranging from $1$ to $n$, discretely). Its return is given by: $$R_p=x_1R_1+\ldots+x_nR_n=\sum_{i=1}^{n}=x_iR_i\...
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