# Questions tagged [mean-reversion]

A mean reverting process is a process that, over time, tends to drift toward its long-term mean.

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81 views

### Hull-White Monte Carlo simulation - mean reversion function

Quite new to implementing Hull white model in Monte Carlo simulation, hope to get help for 1. how to get the function $\theta$ in the following formula (the function used to match initial term ...
46 views

### What's the intuition behind factor grouping?

From the book "Finding Alpha", written by a popular quant fund WorldQuant, explains many techniques about quantitative investing but intentionally omits many of the caveats and applications ...
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### Covariance of mean-reverting Vasicek process?

I am dealing with a mean-reverting Vasicek process defined as: \begin{equation} S_t = S_0 e^{-at} + b(1-e^{(-at)}) + \sigma e^{(-at)} \int_{0}^{t} e^{(-as)} \ W_t \end{equation} I want to ...
180 views

### How to perform Monte Carlo simulations to price a Forward contract under the Schwartz mean reverting model?

Objective: (1) Implement the Euler Explicit Method for solving the PDE for option prices under the Schwartz mean reverting model. (2) Compare with a Monte Carlo simulation. I'm stuck with point 1 (...
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### 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–...
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### Alternative Hurst Exponent methodologies?

The theory behind the Hurst exponent is that every instrument exhibits a certain mix of trending and mean reversion, where Hurst values closer to 1 represent a higher likelihood of trending and Hurst ...
42 views

### Solution to Stock Price SDE with mean reversion [duplicate]

Suppose $S_t$ follows the process (notice the $S_t$ term in the diffusion part): $$S_t := S_0 + \int_{h=t_0}^{h=t}\alpha(\mu -S_h)dh + \int_{h=t_0}^{h=t}\sigma S_h dW(h)$$. I actually don't know how ...
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### The distribution of mean reversion time from the OU process

I was reading the paper Statistical Arbitrage in the US Equity Market and I couldn't understand the figure that plots the histogram of the empirical distribution of characteristic time to mean ...
76 views

### Cointegration stationary test yields different results if the pairs are swapped

I've been backtesting on a spread mean reversion strategy on certain stock pairs. I observe the stationarity via scatterplot and plotting a histogram. Then I verify it using Augmented Dickey Fuller ...
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### Statistical test for comparing two different speed of mean reversion parameters for CIR model

I am trying to compare two different values of speed of mean reversion parameter for CIR model. I would like to know if there exists a statistical test for comparing these two parameters. the estimate ...
400 views

### Can one successfully daytrade 0dte options based on RSI?

I've been doing that manually for 2 months successfully (40% ROI) with SPX 0-1 DTE (Days To Expiration) options, both puts and calls. I might be just lucky so I purchased some data to do backtesting ...
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### Is the rate of reversion of spot variance smaller or greater than the rate of reversion of long-term mean of spot variance?

Is the rate of reversion of spot variance smaller or greater than the rate of reversion of long-term mean of spot variance? In other words, is kappaM>kappa or kappa>kappaM of a two-factor affine ...
26 views

### Distribution of risk factors with mean-reversion properties

I'm trying to figure out a way to determine if a given change in a risk factor, such as a volatility node on a surface, or a basis spread on a curve or an FX rate etc. as well as equity prices can be ...
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### pairs trading algorithm with returns

I'm having a difficulty grasping how to write a pair algorithm using returns instead of prices. With price differences, I have the mean difference over a long time period. When the current price ...
91 views

### What the most general but precise description one can make about mean-reversion and momentum strategies?

Is there anything about this metaphor of momentum and mean-reversion in markets that is more subtle, more general. What factors are amenable to the interpretation? Are people almost always referring ...
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### What is a good way to think about and estimate VIX half life?

Would it make sense to run an AR(1) regression to estimate a beta and then estimate the half life as -ln(2)/beta?
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### Negative values in CIR model

I'm having difficulty understanding the well known property of the CIR model that it can't go below zero. Wikipedia says that this is because the random shock on the rate will grow very small as r ...
91 views

### Mean-reverting backtest between index and components [closed]

I am a beginner with ETF replication: I have to make a code to make the value of my assets go back to the average of the index Eurostoxx 50 with a subset of components. I am not sure how to implement ...
152 views

I am looking to optimize the open/close signals and time for a pairs trading strategy my partner and I are researching. We don't want to go p-hacking so we have been trying to decide: We have 20+ ...
231 views

### Negative Hurst exponent

I am trying to test Hurst exponent in different time lag range. However, i got negative values in some time lag range which is weird, because the Hurst exponent should have values within the range ...
135 views

I'm setting up and following a pair trading operation by the method of summing the distances squared (SSD). After determining the best pairs, I have to track the spread between the normalized prices. ...
58 views

### William K. Bertram's sharpe formula checking

I have some issues to verify by simulation the formulas in the paper of William K. Bertram "Analytic solutions for optimal statistical arbitrage trading". first, the reversion parameter alpha=180 in ...
64 views

### mean reversion model estimation - what method?

how can I estimate this model for mean reversion?
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### Reference on Futures basis trading strategy

I have heard that it is possible to trade on the futures basis. In my understanding, the futures basis is essentially the difference between the futures price and the underlying asset (also referred ...
35 views

### Stochastic process with determinstic frequency of regime changes

Suppose that I have an OU process. For instance, assume that I want to model the interest rates. Suppose that regime change is known ex ante, and is deterministic in terms of frequency (For instance, ...
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### Options Pricing and Mean Reversion

I'm confused about the impact that a mean reverting stock price process has on the value of an option on it. Several sources say that there is indeed an impact on the price of an option: Option ...
311 views

### Expanding window vs Rolling window z-score

I wish to find the z-score of a value measure( e/g P/E ratio) to compare them across asset classes, currently i am using an expanding window z-score to calculate the long-term mean and standard ...
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### Mean Reverting to its own variance?

Good morning all, When trying to decipher some documentation I have come across this stochastic process which seems to me much like a Ornstein-Uhlenbeck (or Vasicek) process. dX_t=-\kappa(X_t-\...
682 views

### Is there a difference between “regression toward the mean” vs “mean reversion”, in the context of financial time series and cash flow analysis?

I read the Wikipedia articles, and it implied that it was different: https://en.wikipedia.org/wiki/Regression_toward_the_mean In finance, the term mean reversion has a different meaning. Jeremy ...
The formula for the mean reversion model in log normal form: $x=\ln(S)$ $x_{i+1} = x_i + [a(m-x_i)-\frac{1}{2}\sigma^2] dt + \sigma \sqrt{dt} \epsilon$ Can this formula be written in exponential ...
I am doing a research exercise where I have two price series $X_t, Y_t$ which I regress against each other and test for cointegration. Once I confirm that they are cointegrated (using CADF or ...