Questions tagged [correlation]

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

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Proving an Identity between a pair of correlated Wiener processes

Suppose we have the following subordinated stochastic differential equations: $dR(t)=\mu dt+\sigma (Y(t))dW_{1}(t)$ $dY(t)=f(Y)dt+g(Y)dW_{2}(t)$, where $W_i$'s are standard Wiener process such that ...
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question about spot/vol correlation

In this paper The Interplay between Stochastic Volatility and Correlations in Equity Autocallables by Alvise De Col, Patrick Kuppinger (2017) https://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
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Literature and Intro to Dispersion Trading

I am familiar with the basic idea of the dispersion trade i.e. index vol vs constituent vol and implied correlation. I am wondering if there are any standard resources (pdfs, books, presentations) ...
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Estimate covariance matrix using prices

We generally estimate the covariance matrix of assets using their returns instead of prices. Why is that the case? I can think of two possible reasons and would appreciate comments/feedback regarding ...
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Portfolio of Assets with non-constant correlation - Maximum Drawdown

How could I calculate the maximum drawdown (given a specified confidence interval, ie. 99%) of a portfolio whose assets have non-constant (deterministic or stochastic) correlation? Is there a ...
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Creating a Covariance Matrix

Lets say that you have the correlation of x,y and you have the standard deviations of x and y , how would you then find the covariance of x,y using the correlation of x,y and and the standard ...
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Two commodities which are normal distributed and perfectly correlated

The daily price change in commodity 1 is distributed $N(0,0.15^2)$ and the daily price change in commodity 2 is distributed $N(0,0.3^2)$. The two commodities are 100% correlated. 1) Does the relative ...
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Sharpe ratio of strategy exploiting correlations that vary by time interval

The Epps effect "is the phenomenon that the empirical correlation between the returns of two different stocks decreases with the length of the interval for which the price changes are measured" (...
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Creating a matrix of average correlations for sub-industry from individual stock correlation matrix

I am having trouble trying to figure out how to do this in Python. I have created it in Excel, but I would like to automate this for any sector or grouping of sub-industries. I first start with ...
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Robust bounds or approximations on implied volatility skew when $\lvert \rho \rvert \rightarrow 1$

Are there any robust / non-parametric results for pure stochastic volatility models, in terms of bounds or preferably accurate approximation, for the implied volatility skew $\partial IV(k) / \partial ...
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Correlation Gold and SPX in BBG

I was always under the impression that gold as a safe haven was more or less inversely correlated to the general market. After using the HRA function in Bloomberg I saw that the correlation is just -...
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Correlation between the perfect market-timing strategy and the market itself?

What would be the correlation between a perfect market-timing strategy [that it always goes long (short) one unit of the market the day before the market goes up (down)] and the market itself, given ...
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Correlation of a portfolio of trading strategies to a benchmark [closed]

I have two trading strategies, both having a correlation of 0.5 to an indicator 'i'. If I take a portfolio of these two strategies, what will be the correlation of this portfolio with the indicator 'i'...
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How to test ESG score as a factor against traditional factors

I have created my own ESG scoring system. I would like to test it as a factor against the traditional factors (growth, Value, quality, size etc) In essence a correlation test. Could anyone please ...
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Negatively Correlated Assets with similar medium-term trends

Theoretically, one could have stock prices with returns $\rho_1(k)$ and $\rho_2(k)$ having mean values $\mu_1$ and $\mu_2$, but still be negatively correlated with $$ \mathbb{E}[(\rho_1(k)-\mu_1)(\...
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Change of measure for BGM (LMM) Model

I've been checking the demos for BGM (LFM) forward rate model. Here's a short reminder to help you follow: Now, take the following $$\frac{dL_j(t)}{L_j(t)} = \sigma_j. dW^j(t) = \mu_{ij} dt + \...
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Questions about beta, correlation, and covariance

Currently, I calculate beta, correlation, and covariance measures using daily log normal returns of Security A and Benchmark A. What would it mean if I were to use daily log normal excess returns in ...
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Relationship between correlations of long only and short only portfolio with long-short portfolio?

I am working on one quality and value factor, the correlation between a long-only or short only portfolio of these two factors is respectively 0.7 and 0.8, and the correlation between combined long-...
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Cega - Correlation Delta from multi-asset derivative

I want to calculate the Cega, i.e. correlation delta, for a multi-asset derivative numerically (the difference of the price from a tiny move in correlation). However, I found it is difficult to follow ...
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129 views

FX Correlation Risk from cross ccy pairs

Suppose you are long a TRYJPY call option. And lets say you can delta hedge using USDTRY, AUDJPY, and AUDUSD. In this case I would delta hedge by buying USDTRY, selling AUDJPY, and buying AUDUSD. If ...
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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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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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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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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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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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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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162 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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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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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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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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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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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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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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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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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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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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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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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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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 market correlation for long / short equity portfolio

Given a long / short equity portfolio, I want to have some net long market exposure. My portfolio volatility is fixed to a target, so I don't think it makes sense to target market beta. I think I ...
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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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154 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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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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