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Questions tagged [correlation]

A measure of the degree of linear association between a pair of random variables.

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Averaging Correlation Matrices based on different Periodicity

Averaging correlation matrices based on different models, but the same data, is commonly done. If the correlation matrices are derived from return series, is it proper/common to also average the ...
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102 views

Dependence of implied volatility on spot-vol correlation

I have the following general SV model: $$ dS = \sigma S dW_S $$ $$ d\sigma = a(\sigma,t) dt + b (\sigma, t) dW_\sigma $$ $$ dW_S dW_\sigma = \rho dt $$ where $a , b$ are deterministic functions of $\...
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Can you derive fx correlations given the historic correlations of base pairs

Say for USDJPY and GBPUSD, I have the historic data and calc the volatility and correlation between these pairs. Because GBPJPY = GBPUSD x USDJPY. Can I calculate the correlation for GBPJPY directly ...
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Analyse correlation between LIBOR (quote in yield) and MSCI AC World (in dollars)

How would you analyse the correlation between LIBOR and MXWD? My initial intention was to get the log return of MXWD and take the opposite of the log return of the LIBOR yield (because when yield ...
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Tools related to Granger Causality

I would like to know if there are some tools that can measure that one time series is "faster" than the second one. I talk about really similar time series related to high frequency trading (hundreds ...
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43 views

serial correlation and CUSUM results

I have the following CUSUM test resulted from autoregressive distributed lag models (ARDL). Does the CUSUM results show that the model is stable? I am a bit confused because the red line in CUSUM ...
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119 views

Find the brownian motion associated to a linear combination of dependant brownian motions

I have $N$ correlated standard one-dimensional Brownian motions $W_1,\ldots,W_N$ with correlation matrix $\rho$ and I consider the process $Z_t \equiv \sum_{i=1}^N \mu_i (t) W_t$ where the $\mu_i$ are ...
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166 views

How to calculate implied correlation via observed market price (Margrabe option)

I can't seem to figure out how to do the following: compute the implied correlation $ρ_{imp}$ by using the observed market price $M_{quote}$ of a Margrabe option, and solving the non-linear equation ...
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Do correlated assets affect the price of a portfolio of derivatives?

I need to compute the value at risk of a given portfolio as an exercise for a class at university but I have trouble understanding how correlated assets affect the price of the portfolio. Could you ...
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57 views

Some basic examples for Granger causality

I have two time series, X and Y. The number of observations in each time series is the same and the variables would be price(logged). The goal of my research is to analyze if one variable X follows ...
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34 views

CFD broler spread as indicator for stock market

Retail trader on stock market has very limited ability to accomodate huge amount of information, it leds me to idea of using behavioir of more informed players - CFD brokers - spread of their CFD ...
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37 views

CDF&density of stock price modeled by standard brownian motion

Assume that the price of the stock follows the model $S(t) = S(0) exp ( mt − ((σ^2)/2 ) t + σW(t) )$ , (1) where W(t) is a standard Brownian motion; σ > 0, S(0) > 0, m are some constants. Derive the ...
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Do you have any examples of 2 assets that are non linearly correlated? And any models that calculate portfolio risk based on non-linear correlation?

Do you have any examples of 2 assets that are non linearly correlated? And any models that calculate portfolio risk based on non-linear correlation?
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Detecting leading stocks using lag correlation

I am working on a project to find leading stocks in a stock market by using lag correlation. Say I want to compare 2 stocks, X and Y, and I have the time series of stock prices. Assume that the ...
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Binomial correlation measure in the trivariate case

I have a question about the binomial correlation measure at page 530 in Hull(2009), Options futures and other derivatives (7th Edition) which is defined for the bivariate case as: $\beta_{AB}(T)=\...
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104 views

Difference between volatility measures of a basket of assets

I am trying to understand intuitively the difference between two different measures of realized variance of a basket of assets. The first measure I am aware of is when you take the realized variance ...
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149 views

Correlation sensitivity of Rainbow options

I read from various sources (eg. Exotic Options and Hybrids, M. Bouzoubaa) that the correlation sensitivity of Rainbow options (say a call price on a basket made of 50% of the best stock, 20% of the ...
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target correlation for portfolio

Given a long / short equity portfolio, I want to have some net long exposure. My portfolio volatility is fixed to a target, so in trying to have a certain beta to the market, the only thing I can ...
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Parametric VaR assumption question

Why do you have to make a correlation matrix when calculating the parametric value at risk, if one of the assumptions for this method to work is that the assets of the portfolio must be independently ...
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1answer
88 views

Showing the Gaussian shift theorem for bivariate case

I was reading about the Gaussian shift theorem in "An Introduction to Exotic Option Pricing" by Peter Buchen and came across a question that I can't seem to figure. In the book, he uses F(Z) (a ...
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137 views

How to calculate correlation between commodities with forward prices?

I'm trying to understand which is the correct way to calculate the correlation between 2 commodities with forward prices. My idea would be first bootstrap forward prices to have only spot prices for ...
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137 views

Minimizing Correlation to Index

In his PhD thesis in the chapter Market Neutral Portfolios, page 69, [1] Valle sets up an optimization problem which minimizes the absolute correlation of the portfolio log returns to the log returns ...
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Sharpe Ratio with Stochastic Interest Rate?

All versions of the Sharpe ratio that I've seen seem to assume that the risk-free rate is constant, and the standard deviation of the excess return in the denominator simplifies to the standard ...
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Correlation among different sectors of the market

It is known that many sectors/industries within the stock market are correlated with each other. For example, using VIF as a measure of correlation, I have the following result: ...
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calibrating two (or X) equity diffusion trees

I have two equities S1 and S2. Each one follows the following tree evolution : $$S_1 \rightarrow \left \{ \begin{matrix} S_1 (1+u_1) & \text{with probability } p_1 \\ S_1 (1-d_1)...
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92 views

Preference between low (zero) and negative correlation

I am trying to create an artificial score grading user's portfolio correlation. In terms of diversification, lower correlation is obviously better. However, should negative correlation get a higher ...
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140 views

How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?

Introduction My goal is to retrieve a single Value-at-Risk (VaR) of a N(0, H) random variable $X$ at the $\alpha \in (0,1)$ confidence level where H is a known d-dimensional positive definite matrix ...
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Correlation between a sector and MSCI ACWI returns

I have daily return data of 11 sectors of MSCI World Index and the MSCI ACWI index. I want to know the stationarity of correlations between the sectors and MSCI ACWI index. This is what I have done: ...
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179 views

Portfolio correlation of a long-short portfolio

I have a portfolio of long/short positions in stocks. I would like to calculate the portfolio correlation. Should I somehow account for the short position while calculating the portfolio correlation? ...
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187 views

Futures and Forward Prices vs interest rates

Textbooks usually state that if an asset's prices are positively correlated with interest rate movements, then its Futures price is going to be greater than its Forward Price assuming the same ...
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93 views

correlation in time series analysis

the goal of my research is to analyze if one variable X follows the movement of another variable Y over time. Meaning that Y is slightly ahead of X. The number of observations in each time series is ...
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87 views

Correlation basket equities

One question: when asking for the correlation of a basket, a trader told me 50% whereas I expected him to give me asset pairwise correlations (i.e. the correlation matrix). What does this 50% mean ...
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275 views

Correlation of assets to portfolio of assets

How do you calculate the correlation of an asset to a portfolio, when for all assets in the portfolio you know there: correlation to each other, volatility and weight in portfolio. For example: ...
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251 views

Which program for a DCC-MIDAS model?

for a thesis research, I plan to use a DCC-MIDAS model. The program I was working with (STATA) is not able to run this. Do you have any suggestions as to which program is best for this analysis? ...
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111 views

Spot variance drift consequently to style drift

I am looking for some information on how to spot variance drift for a portfolio in accordance to its benchmarks, Let's say that we have returns of the portfolio $\textbf{P}=(P_1,...,P_t,...,P_n)$ and ...
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148 views

Simulate double exponential process with correlated jumps?

So, I'm trying to simulate a correlated double exponential jump process for two assets, and I understand the pure exponential jump process ($\eta_1$ and $\eta_2$, the probability of an upward jump ...
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55 views

What are the reasons that make stock return - bond yield correlation a meaningful one?

I have come across interesting charts that show the changing correlation between stock returns and government bond yields. My gut instinct tells me that such relationship would be expected to be ...
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87 views

Bivariate risk neutral distribution through copula

I want to build a bivariate risk-neutral distribution from two liquid assets (A and B) through the use of a copula. As A and B are liquid, I have the marginal distributions from the market. All I have ...
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457 views

Monte-Carlo simulation Hull-White process

I have one question about Monte-Carlo simulation Hull-White process, maybe you can give me some advice. I constructed a Hull-White process using Python and QuantLib. Now I want to construct a Hull-...
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177 views

generating a correlated RV which has the same correlation to existing samples

Suppose I have generated a collection of correlated sequences of samples $(S_i)_{i=1}^{n}$ from random variables $\mathbf{\underline{x}} = x_i$. Let's fix a sequence of reals $(\sigma_i)_{i=0}^{n}$. ...
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234 views

Dollar Index vs Hang Seng Index: Negative correlation, but what's driving it?

I recently read an article which highlighted that a weaker dollar tends to coincide with rallies in Hong Kong stocks. I did some quick analysis: I calculated monthly returns on the Dollar Index and ...
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211 views

Correlation Oil Price with Bond Fund - question on how to tackle this

I am trying to assess the sensitivity of a bond portfolio to the price of oil. The first intention was to 1. Get brent prices (CO1) for say a period of 5 years and 2.Get prices of each bond for the ...
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389 views

Quanto effect in cross currency mtm swaps

Apparently the standard way to value these swaps involves ignoring the quanto effect, - ie the correlation between fx and rates. I wonder why this is - is this correl always so close to zero? Eg of ...
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118 views

Correlation between bond yields and stock returns?

I intend to regress the correlation coefficient (rolling window and/or DCC) between NIKKEI 225 adjusted close and 10yr Japanese government bonds on inflation , inflation expectations and other factor ...
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1k views

Correlated assets in Monte Carlo simulation

I'm trying to simulate $N$ correlated assets in Excel in order to estimate a basket option price. For 2 assets, I correlated the two random variables $X_1$ and $X_2$ and then simulate the ...
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107 views

How to calculate the contribution (%) of an asset to the global correlation of the portfolio?

I have a portfolio X with weights $w_i$. I am trying to find the contribution $\xi_i$ of asset $i$ to the total correlation $\rho_{XM}$ of the portfolio X to an index M. I can't find these ...
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126 views

Ordered correlated random numbers

I'm not sure how feasible this is. I'm aware of how to generate correlated random numbers using a cholesky decomposition. However, say I have a fixed data set in increasing order (e.g. Price series: $...
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Calculate price variance caused by denominating currency

I would like to calculate asset correlations while excluding movements resulting from the denominating currency (as much as possible). My common sense tells me that any two assets with the same ...
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169 views

Implied correlation

Have I understood it correctly if the standard way to calculate implied correlation is the Gaussian Copula model where we: Calibrate the underlying portfolio to get a homogenous default probability ...
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227 views

Correlation between equity returns and debt spread changes

I have got two rather short questions. Statement: Theoretically, a firm's equity prices and credit spreads should be negatively correlated. This correlation tends to be stronger for riskier companies....