Questions tagged [correlation]

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

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How does the implied correlation change when the spot price of the Basket Call/ Put option goes up?

Given a basket Call/Put: $BasketCall_{payoff} = max[0, \Sigma^n_{i=1} w_iS_i(T) - K]$ If the spot price of the basket goes up/down, how would the implied correlation change? I guess what I am not ...
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38 views

Variance swap correlation trade

I found two highly correlated assets that have spread in 3M realized and implied vol at historical minimum. To go long on this spread I thought of using two variance swaps. Would it be cheaper to ...
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97 views

Calculating Correlation of Two portfolios?

So I'd like some help w/ this question. Given 3 assets with means, variances, and correlation: Two portfolios are created (A and B), each with the three assets above with weights ($w_n$) as follows: ...
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negative correlation between EBIT and sales in Altman's Z

In his 1968 paper, Altman found that sales volume (i.e., sales divided by total assets) is a useful predictor not by itself, but as a suppressor variable to improve the predictive power of EBIT/TA. ...
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38 views

Equal weight correlation swap payoff derivation

I am aware that the payoff for a equal weighted correlation swap is; $$ (\rho_K-\rho)*\text{Notional} $$ where $$ \rho = \frac{2} {n(n-1)}\sum_{i < j} \rho_{ij} $$ I am wondering how I can derive ...
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101 views

Brownian Motions theorems

I know that if $W$ and $W′$ are two independent brownian motions, then $dWt \ dWt′$ = 0. How can I prove/demonstrate this theorem? Additionaly, how can we prove that if $W$ and $W′$ are dependent, ...
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51 views

Average portfolio correlation vs. external metric

I am coming across a problem I can't seem to wrap my head around, and I am not sure I am using the right words so cannot find much info in it! I have a portfolio of assets, with data on historical ...
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139 views

Correlation between stock prices given correlation between returns

assume I have two stocks with known volatilities and a known correlation coefficient of returns - does anyone know how to determine the correlation between the prices and NOT THE RETURNS
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61 views

Correlation between Two Factor Gaussian Shortrate Model and Black Scholes Model

I want to implement a two factor Gaussian Shortrate Model \begin{align} r(t) & = x(t) + y(t) + \phi(t), \\ dx(t) & = -ax(t)dt + \sigma dB_1 (t), \\ dy(t) & = -by(t)dt + \eta dB_2(t), \end{...
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50 views

Correlations between different baskets of assets

Struggling to see the answer to the following problem - Assume you have $N$ different assets, and all pair-correlation coefficients $\rho_{ij}$ between them are known. If you now form two arithmetic ...
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66 views

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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154 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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45 views

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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45 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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124 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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184 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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127 views

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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73 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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35 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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109 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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166 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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36 views

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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97 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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149 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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148 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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71 views

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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80 views

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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97 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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150 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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205 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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325 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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97 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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99 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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321 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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285 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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112 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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158 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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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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486 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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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 $(\sigma_i)_{i=0}^{n}$. ...