Questions tagged [correlation]
A measure of the degree of linear association between a pair of random variables.
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Calculation of break-even correlation for diversification effect in N-assets case?
I'm thinking about a generalization of the following case: for 2 assets, there is a diversification effect as soon as i obtain a positive weight for the minimum-variance portfolio in the asset with ...
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A term to compare 2 stocks based on simultaneous trending and ranging characteristics
There a 2 stocks called A and B. We take a look at the daily chart of both stocks over the last 1 year. On 90% of the days A and B both trended or at least one of A or B trended. On 10% of days both ...
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Correlation risk between protection (seller) and reference entity
I am learning about central clearing.
In my understanding, CDS are usually cleared via central clearing.
But at the same time I heard that in case of too much correlation such as US bank selling ...
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LMM (Libor market Model) Correlation Calibration
I use a LMM model from a well known vendor, using a SOFR swap curve and SOFR swaptions. The calibration set include many/all of the ATM swaptions from 1m-1y to 30y-30y and I get a very good fit for ...
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How can this problem be defined formally?
Let's consider a straightforward example in which I possess a portfolio consisting of two stocks:
$
R(t) = S_{1}(t) \cdot x_1 + S_{2}(t) \cdot x_2,
$
Here, $t$ represents the time index, $R(t)$ ...
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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:
$$
\begin{bmatrix}
<\text{spot, spot}> & <\text{atmv, spot}> \\
<\...
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Stochastic process for modelling correlation?
This question relates to Financial Machine Learning, and more specifically to competitions like Numerai.
In this competition we have a dataset X and a target y (return over a given horizon). The ...
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Monte-Carlo method for multi-asset pricing
As I was working on this paper https://hal.science/hal-00319947/document by Emmanuel Gobet, I came across this paragraph that says to price a barrier option on (for example) two correlated assets, you ...
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How do your solve for trader's optimal demand in market similar to Kyle's model?
Suppose that $(\Omega,\mathcal{F},\mathbb{P})$ is a standard probability space and $Z_t=(Z_t^1,Z_t^2)$ is a two dimensional Brownian motion with the filtration $\mathcal{F}^Z_{t}$ and $Z_t^1$, $Z_t^2$ ...
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How to hedge a dual digital option
Let us assume we have two FX rates: $ 1 EUR = S_t^{(1)} USD$ and $ 1 GBP=S_t^{(2)} USD $. Let $K_1>0, K_2>0$ be strictly positive values and a payoff at some time $ T>0 $ (called maturity) ...
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Maximum likelihood estimation of system of correlated SDEs
I have the following system of SDEs (which you can think of as 3 different stocks)
$$dX_t^1 = \mu_t X_t^1 dt + \sigma_t X_t^1 dW_t^1$$
$$dX_t^2 = \mu_2 dt + \sigma_2 dW_t^2$$
$$dX_t^3 = \mu_3 dt + \...
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How would I find correlation / association of different time series datapoints with a target variable?
the title is a bit confusing.
Functionally, I have a dataset of N stocks containing options information, short information, and earnings information for each of the N stocks.
For each unique stock in ...
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If returns are correlated, are Sharpe ratios correlated?
Suppose we have two correlated return series:
$$a \sim N(\mu_a,\sigma_a^2)$$
$$b \sim N(\mu_b,\sigma_b^2)$$
$$correl(a,b)=\rho$$
The sample Sharpe ratios of the two series, after $t$ samples for $t \...
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RiskMetrics Half-Life and Decay Factor Settings
I have been reading about the RiskMetrics methodology. I read that RiskMetrics recommend a lambda of 0.94 for daily data and 0.97 for monthly data. I would like to convert these numbers to half-lives. ...
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correlation of 1/X [closed]
My question is the following.
If the correlation between the log-returns of X and Y is rho, what would be the correlation between the log returns of 1/X and Y ?
Thanks for your answers.
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hedging out of cross-ccy vol risk using direct ccy options [closed]
Lets suppose a G10 FX vol market-maker starts out with a flat book. During the day, the market-maker bought a EURUSD 1 week ATM straddle from one client while sold USDJPY 1 week ATM straddle from ...
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Alternative To Granger Causality?
Are there any other mathematical tests besides Granger that quants use to determine casual relations between two time series? If so what are they? How about convergent cross mapping?
Thanks
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Correlation with Differ Units of Measurement [closed]
I was wondering how to accurately get the correlation between a variable of percent change return and a variable of dollar change or basis points. Should I standardize both variables or will that lose ...
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Correlation between CDS return relevance
I see that there is much literature that uses the correlation notion in the equity returns to construct a graph or look into how they are related to one another. If we want to extend this to Credit ...
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Mean-variance framework with endogenous correlations
In most mean-variance frameworks I have seen, once we clear markets in the model, it determines asset prices (and returns). However, all of these frameworks assume that the correlation matrix of the ...
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Cholesky decomposition reduces volatility of simulated Wiener Process / Brownian Motions
I am trying to simulate $n$ correlated geometric brownian motions (GBM) given a specified correlation matrix $\Sigma$ by following this procedure which uses Cholesky decomposition.
However, when I ...
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Techniques for proxying time series / stock prices
What are some good techniques for proxying time series?
My purpose is for risk management / modelling and I would like proxy to missing series.
Given that I also have to account for volatility, ...
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Local volatility implied spot vol correlation
I have a question about local volatility models.
In a lot of articles it is stated that the implied spot vol correlation of this model is -1 and we usually compare this with stochastic volatility ...
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Simulating Correlation (but sample correlation is always too low)
I am trying to simulate correlation in order to price a correlation swap (via Monte-Carlo). For simplicity, let's assume we have 2 assets, and everything is correlated with $\rho$, and there is no ...
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How to optimize two highly correlated risky assets?
Suppose you have two highly correlated risky assets.
Correlation coefficient: 0.9
Volatility:
Asset 1 price varies 2.5% /day
Asset 2 price varies 5% / day
What can be done to do reduce the risk and ...
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What's the right autocorrelation formula?
I'm trying to see the influence of autocorrelation in my processes and to do so I have to compute it, however it seems to be hard to find a coherent formula over the web. I found pretty much two ...
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Correlation between fundamental and market data
I got hold of a data set which contains fundamental data like analyst recommendations/revisions (consensus only) and I am trying to come up with an idea of how this could be used as a trading signal ...
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Correlation Size
If I want to make an argument that two stocks are reasonably correlated:
Q1. What is the most credible source (most cited) of correlation size for stock return pairs? What is a reasonable small, ...
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Adjusting a correlation matrix based on one changed correlation
I have a correlation matrix that is created by historical asset returns, but I want to see how changing one of those correlations would affect the rest of the correlation matrix. How would I go ...
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Does correlation of stocks represent magnitude?
When calculating the correlation between two stocks I get an 85% correlation.
Does this indicate anything about the amount the stocks are going up (so if one goes up 10% so does the other) or just ...
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On moving Linear Correlation (rolling correlation)
Let's say I have two random variables $X$ and $Y$ which each represents the daily returns of two given stocks. I can easy calculate their (total) correlation by finding their covariance matrix $\Sigma[...
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Two sound waves in phase at different lags with varying signs?
I have two interest rate time series but want to think of this as sound signals for thought purposes.
Imagine you have two time series of audio signals. You run a time lagged cross correlation ...
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Interpreting the average correlation figure in Pozzi et al. (2013) paper
Has anyone read the paper "Spread of risk across financial markets:better to invest in the peripheries" by F. Pozzi, T. Di Matteo & T. Aste? If so, how do you interpret equation (1) in ...
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Estimation of copula for discrete random variable
I'm interested in the estimation of parameter of copula for discrete random variables.
The problem is described as follow:
I have 30 discrete random variables $X_1,.., X_{30}$, each random variable is ...
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Lemma (maybe) to imply the sign of the sensitivity to correlation
Can anybody please help me to understaind if this result is true ?
Let $\pi=\mathbb{E}\left(f(X_{T})g(Y_{T})\right)$
where $f$ and $g$ are increasing functions.
Hence, $\pi$ is increasing with respect ...
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Simulating Correlated Stock Returns in Python (SciPy)
I'm looking to generate stock returns with inter-stock correlation in Python. However, the output is not behaving properly and may have accidental temporal correlation causing issues.
This code is ...
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Kelly Criterion for Multiple Simultaneous Correlated Bets [closed]
I am looking for an equation for the optimal fractional bet sizing for N number of simultaneous correlated bets.
I am looking specifically for an equation for binary bets, but an equation for bets ...
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How to simulate correlated stock prices (not returns)
Suppose we have two stocks following GBMs. Drift and volatility are calculated based on historical data. Furthermore the stocks are assumed to be correlated (i.e. they move together, if stock 1 goes ...
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GBM drift when simulating correlation betwenn GBM with Cholesky Decomposition
I am currently trying to simulate correlated GBM paths and I found the Cholesky Composition for it. From my understanding, the Cholesky Decomposition can be used to create correlated random variables ...
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Examining the dependence of the fractional difference parameter in ARFIMA(0,d,0) vs bar size for Realized Volatility
Realized volatility is a long-memory process and so I fitted an ARFIMA(0,d,0) to log(RV15) where RV15 is realized volatility calculated from 15-min bars. I proceeded to examine how changing the bar ...
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Information Coefficient (IC) Formulae Differences
I am learning about Fundamental Law of Active Management, and there seems to be two different Information Coefficient (IC) formulae presented.
Though I myself am not a CFA candidate, these appear to ...
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How to properly calculate the average across multiple correlations?
I'm trying to obtain an average across 3 correlations.
Using Python, I obtain these correlations with:
corr = df.apply(lambda s: df.corrwith(s))
which outputs:
<...
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Beginner's resources on copulas and impact of correlation on loan defaults?
I'm hoping this question is not too banal or off-topic for this forum.
Could you please help me understand / point me towards some resources on the impact of correlation on loan defaults?
First ...
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Correlation between corporate bonds and treasury
What aspects decide the correlation between US corporate bonds and US treasury ? I was told that some corporate bonds are more sensitive to treasury than others. Sectors or maturity?
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Find k of n assets that "minimize" the correlation matrix
I'm trying to find an efficient way to select $k$ from $n$ risky assets that are the least correlated with each other. I know that I can perform a brute-force search of all $k$-sized combinations of ...
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How to extract informative value from correlations of assets? Subadditivity of correlation calculation an issue
I was reading Nassim Taleb's Paper: Fooled by Correlation and found it very informative. I had always struggled with finding value in correlation in Finance, especially seeing a lot of bad ...
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Hedge 3 securities against 3 other securities
I have a portfolio of 6 securities, 3 long 3 short. I need to hedge them against each other so directional exposure = 0. How would I decide how to weight each security?
Is there a model to do this?
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Contribution to Mahalanobis Distance
I am using Mahalanobis Distance to measure abnormal behavior within a portfolio consisting of a handful of general asset types, and am trying to figure out how to decompose this measurement into ...
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Correlation between brownian motions and Cholesky decomposition [closed]
I know it is a pretty basic question (I'm new at Quantitative Finance), but what's the logic behind the Brownian Motions correlation?
The expression is:
Where is this formula coming from?
On the ...
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Sensitivity of correlation swaps to stochastic volatility
Are correlation swaps sensitive to stochastic volatility? Can you please justify from a theoretical point of view?
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