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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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1 answer
71 views

Pairs trading with 3+ assets

I am trying to understand how you would construct a pairs trading strategy on 3+ assets. In the 2 asset case, assuming zero drift, we trade based on: $$dX_t = \beta_AdS_t^A - \beta_B dS_t^B,$$ where $\...
1 vote
2 answers
587 views

Impact of correlation on greeks of a multi-underlying autocallable product

Please could someone explain how the greeks (especially the delta) of a multi-underlying autocallable product (i.e. an autocall on a basket) change when the correlation of the underlyings fluctuates? ...
0 votes
0 answers
34 views

Instantaneous correlation and terminal correlation - 6.29

I am trying to derive the $(6.29)$ equation from brigo and Mercurio book. We have $dF_2(t)= \sigma_{2,\beta(t)}F_2(t)dW_2(t)$ $dF_3(t)= \frac{\delta_3\sigma_{3,\beta(t)}^2F_3^2(t)}{1+\...
1 vote
1 answer
387 views

Simulating correlated Geometric Brownian Motion with lag

I know that it is possible to simulate two correlated GBM in e.g. Matlab (Generating Correlated Asset Paths in MATLAB) based on cholesky decomposition. However, they take as input the correlation ...
1 vote
2 answers
473 views

Is "Information Coefficient" correlation or rank correlation?

From the textbook, information coefficient (IC) is a measure of the depth of an active manager’s skill. On a more formal basis, IC measures the “correlation” between actual returns and those predicted ...
3 votes
1 answer
237 views

Admissible values for non diagonal elements of correlation matrix

Preparing for possible job market interview questions I was reading some questions on the site. Regarding this question with its solution interview questions Question Let $\mathbf{C}$ be a $n\times n$...
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1 answer
119 views

How to construct a delta-neutral portfolio containing stocks using correlations?

I’m aware of the mean-variance framework where we construct a portfolio such that we attempt to minimise the variance and maximise returns. What if instead we’re in a scenario where the main goal is ...
0 votes
1 answer
119 views

PCA factors not uncorrelated

I ran into an interesting case recently. I am trying to construct a set of uncorrelated factors for a statistical factor model. I have started with picking a certain amount of assets (indices) which I ...
0 votes
1 answer
179 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}> \\ <\...
1 vote
0 answers
86 views

short-term statistical factor models for equities with different trading hours

I wonder if there are existing theory/literature about estimating a short-term statistical factor models for equities with different trading hours. For example if we are estimating a universe with US ...
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0 answers
44 views

Why didn't LMT stock spike and NOC dip in 1990 due to the F-22 raptor competition?

Disclaimer, I am a newbie at finance! I have been tracking the NOC and LMT stock prices and I have a few questions. Both companies seem to be moving together in terms of stock prices. I would expect ...
1 vote
0 answers
85 views

Correlation between a stock and the index without the stock

The weight of stock i in index m is w. The returns are, respectively, r(i) and r(m). I know the volatility s(i) of i, the volatility s(m) of m and the correlation rho(i, m) between i and m. The index ...
0 votes
1 answer
116 views

How do I measure the "dispersions" of a group of stock returns

I have $n$ stock return time series $X_1, X_2, ... X_n$. I want to measure how much they have "dispersed" over time. i.e. are they moving "more together" in 2023, comparing to 2022....
4 votes
2 answers
347 views

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 ...
2 votes
0 answers
703 views

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) ...
2 votes
1 answer
205 views

How to design a strategy whose PnL is proportion to correlation?

I'm reading about this correlation breakout strategy, whose pnl is proportional to $$E[PnL] \sim (\rho_{1D} - \rho_{2D})\sigma_1 \sigma_2$$ where $\rho_{1D}$ is the correlation of daily returns, and $\...
3 votes
2 answers
3k views

How to annualize the correlation matrix?

If asset returns are daily, and the asset return covariance matrix, $\Sigma$, is annualized by $\Sigma \times 252$, do I also multiply the correlation matrix by 252 to annualize it?
1 vote
0 answers
82 views

Discuss how you would allocate your budget between the two assets if their correlation is 1, 0, or -1

An asset A is expected to yield a $2\%$ return with a standard deviation of $1\%$, and another asset B is expected to yield a $1\%$ return with a standard deviation of $1\%$. Discuss how you would ...
0 votes
1 answer
113 views

Analytic Hull White model with correlated stochastic processes

I am trying to price a path dependent option which uses two underlyings (a stock index and an interest rate index). I am using Hull White model for interest rate modelling and local vol for stock ...
0 votes
1 answer
152 views

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 ...
6 votes
1 answer
996 views

Rank Correlation Based Prediction

Are there any methods of prediction (machine learning, regression, etc.) which are designed to maximize the rank correlation (spearman correlation, kendall's tau, etc.) of your prediction with your ...
0 votes
0 answers
33 views

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 ...
0 votes
0 answers
41 views

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 ...
0 votes
0 answers
117 views

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 ...
0 votes
1 answer
138 views

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, $R(t)$ ...
0 votes
1 answer
123 views

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 ...
3 votes
0 answers
80 views

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 ...
2 votes
1 answer
276 views

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 $Z_t^1$, $Z_t^2$ ...
1 vote
1 answer
709 views

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) ...
0 votes
2 answers
289 views

comparing volatility and correlation over time

I'm trying to figure out if some emerging markets change over time. First of all I am going to check for changes in volatility. What would be a good method to do this. And do you suggest comparing ...
0 votes
0 answers
88 views

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 + \...
0 votes
1 answer
761 views

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 ...
1 vote
1 answer
626 views

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 ...
4 votes
1 answer
604 views

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 \...
1 vote
0 answers
327 views

Why is credit exposure higher for a smaller probability of default than for a larger default?

I'm having trouble grasping this concept; I don't see the relevance of the explanation given in the text (Gregory, Counterparty Credit Risk and CVA) either. When expected exposure and probability of ...
0 votes
0 answers
130 views

Wrong way risk exotic option

I've priced an exotic option with Monte Carlo method under the Heston model. Then I want to estimate Wrong way risk. In a paper I've found this method to calculate WWR: WWR can be modeled by means of ...
3 votes
0 answers
240 views

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 + \...
1 vote
1 answer
2k views

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. ...
0 votes
1 answer
111 views

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.
0 votes
1 answer
399 views

Pairs Trading: Normalized price series (co-integrated and correlated) always end up diverging

Need some expert advice and suggestions: I am trying out pairs trading or statistical arbitrage (as traders say). But even if two price series are co-integrated (ADF test, Hurst exponent, Ornstein–...
1 vote
2 answers
180 views

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 ...
1 vote
0 answers
107 views

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
1 vote
1 answer
160 views

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 ...
1 vote
0 answers
70 views

CFD broker 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 ...
2 votes
1 answer
290 views

Autocall- equity/funding correlation

Could someone explain how the price of an autocall changes with equity/funding correlation, please? I have sometimes heard that the trader who sells an autocall is long equity/funding correlation but ...
0 votes
2 answers
96 views

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 ...
2 votes
1 answer
378 views

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 ...
1 vote
0 answers
110 views

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, ...
2 votes
0 answers
516 views

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 ...
0 votes
1 answer
194 views

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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