Questions tagged [mean-reversion]
A mean reverting process is a process that, over time, tends to drift toward its long-term mean.
121 questions
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Does it makes sense to use GARCH to measure mean reversion?
I am doing my final paper at my bachelor. For this, I am testing mean reversion in an asset. I found this paper (Mean reversion in international markets: evidence
from G.A.R.C.H. and half-life ...
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How can one calculate third and fourth moments of a jump-diffusion process with time-varying parameters?
Suppose that $x_t$ is a random process that satisfies the mean-reversion jump-diffusion process governed by the stochastic differential equation
$$dx_t=\alpha(t)(\beta(t)-x_t)\,dt+\sigma(t)\,dW_t+J_t\,...
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zero-crossing variant of pairs trading
The concept of zero-crossing was suggested in Does Simple Pairs Trading Still Work?, July 2010, Financial Analysts Journal 66(4)
by Binh Huu Do and Robert Faff link to paper
The idea is to select ...
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How to estimate the Mean reversion
I am looking for some insights and worked-out example on how exactly should I estimate the Mean reversion parameter of the One factor Hull White model
This link suggests to fit some regression ...
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Is it possible to discretize OU with a more general AR(p) / ARMA (p,q) models?
The discrete analogue of an OU process is a simple AR(1) model. More general AR(p) or ARMA(p,q) models can also be regarded as discrete analogues of an OU process? If so, which coefficients describe ...
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Mean reversion factor logic
I have a hard time understanding the caveats of mean reversion factor logic.
Let's imagine a mean reverting process:
$$
dx_t = θ(μ−x_t)dt+e_t
$$
Where θ is the "mean reversion" coefficient, ...
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Why does AR(1) model with a small coefficient exhibit faster mean-reversion than one with a greater coefficient (when |$\beta$|<1)? [closed]
Suppose we have two mean-reverting AR(1) models, given by
$$X_{t}=\beta X_{t-1}+\epsilon_t,$$
where $|\beta|<1$.
How fast series reverts to its mean is determined by the coefficient $\beta$. As far ...
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Interpretation and intuition behind half-life of a mean reverting process
I am struggling to understand the intuition and use of half-life period of a mean reverting process. According to definition, half-life period shows how long it takes for a time series to return ...
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What is the common accepted/ best performed method to classify trends and mean-reversion for fixed peroid?
I have knew some strategies only work on trends peroid, and other only works on mean-reversion peroid. But I didn't find how to classify trends and mean-reversion.
I wonder the best performed/verified ...
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portfolio weights based on past returns
In the academic paper Industries and Stock Return Reversals by Hameed and Mian (JFQA,2015) (see picture below), the authors describe a trading strategy based on reversal, which essentially buys past ...
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Determine Dependent Variable Product
Let's say I have three products that are correlated (e.g. AAPL, MSFT, and AMZN). I would like to construct a spread between these products and trade the mean-reverting spread. Specifically, sell the ...
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Linear Regression Cointegration Strategy
When doing linear regression to figure out the hedge ratio for the cointegration relationship what does it mean if the residuals are stationary but end up looking like the price time series of y? How ...
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Converting Annual Vol to Instantaneous Vol with Mean Reversion [closed]
Options Pricing and Mean Reversion
In the question above, in the accepted answer, the writer claims:
"For instance with a 100% mean reversion a 20% historical annual standard deviation would ...
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Generalizing a hidden semi-Markov model for trading
Taken from Wikipedia:
A hidden semi-Markov model (HSMM) is a statistical model with the same
structure as a hidden Markov model except that the unobservable
process is semi-Markov rather than Markov. ...
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Why aren't the optimal entry/exit thresholds for OU pairs trading relatively invariant to shifts in the OU mean?
The optimal entry/exit thresholds for mean reversion trading (assuming an underlying Ornstein-Uhlenbeck (OU) process) is derived in the paper "Optimal Mean Reversion Trading with Transaction ...
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StatArb : Fourier transform to find the perfect factor?
We have a basic mean reverting strategy. Given a bench of assets, we are looking for the best linear combination of them such as the resulting normalized time series would be noisy at high frequencies ...
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How to predict a portfolio's reversion?
Sorry if this has been asked before. I've been baffled by a question I'm facing.
Assuming I know there are some certain demands for some stocks in near future, and I put them in a basket as a ...
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Trading based on the log return series
A common strategy in trading is to use a bollinger band system. Simply put, we bet on reversion to the mean and take the opposite trade to the current movement under the assumption a move is overdone.
...
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Mean Reversion without Bollinger Band
What are the ways one can trade mean reversion apart from using Bollinger Bands?
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Dumb question : under the assumption of the normal distribution and using log return stationarity
Under the assumption of the normal distribution, I'm trying to create a single stock mean reversion strategy. I took the log returns because they are stationary, I standardized them and used the ...
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Why do I need fancy methods to calculate half-life of mean reversion?
I am investigating ways to calculate the mean reversion half life of a mean reverting series. I am encountering things like the Ornstein – Uhlenbeck Process and various types of regression to estimate ...
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Correlation between fundamental and market data
I got hold of a data set which contains fundamental data like analyst recommendations/revisions (consensus only) and I am trying to come up with an idea of how this could be used as a trading signal ...
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Why is my mean-reversion half-life completely wrong?
I am using a couple of resources (here and here) to calculate the mean reversion half-life of a time series. This method of calculating it is also presented in Ernest Chan's Algorithmic Trading on ...
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How to incorporate momentum in Ornstein Uhlenbeck to capture overshooting in financial markets?
In modelling asset prices, it is a good idea to model it using a fair value or target price concept. Recently Carr & Prado explored this idea to find optimal stop loss/take profit levels when the ...
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How to derive a pricing PDE for an asset that follows a mean-reverting process?
I want to derive a Black-Scholes type partial differential equation to price options on an asset that follows a mean-reverting process (Schwartz model).
My attempt follows the methodology of deriving ...
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Question about calendar spread mean-reversion strategy
I'm excited to ask my first question here! I'll try to describe the mean-reversion strategy with some background, then explain what I couldn't understand.
The strategy is described in Earnest Chan's ...
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Calibrating OU parameters using AR(1)
I have a mean reverting time series and want to find the Ornstein-Uhlenbeck (OU) parameters of it. I researched the internet and found that we can calibrate the model as a simple AR(1) process,
$$\...
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600
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Simulating exponential Vasicek/Ornstein-Uhlenbeck
I am trying to simulate commodity prices using the exponential Vasicek/Ornstein-Uhlenbeck model from Schwartz 1997 p. 926 Equation (1). I am using the closed form solution from Vega 2018 p. 5 Equation ...
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Estimating Ornstein-Uhlenbeck process drift
What is the easiest way to obtain a drift parameter of O-U process given I have $\mu$?
Is it ok to linearize the O-U process like so:
$P_{t} = \mu + \phi(P_{t-1}-\mu)+\xi_t$
Form vectors from historic ...
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Hull white model calibration - constant mean reverse factor and sigma
I setup a HW 1F model using Monte Carlo simulation with constant mean reversion and volatility factors. When I calibrate to a series of swaptions ( 1x4yr;2x3yr;3x2yr;4x1yr),the last three swaption ...
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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 ...
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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 ...
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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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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 ...
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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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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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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 ...
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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 ...
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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 ...
2
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309
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Pairs Trading parameters
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+ ...
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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 ...
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Pairs Trading situation with spread changes
I'm setting up pairs trades by summing the distances squared (SSD). After determining the best pairs, I have to track the spread between the normalized prices. Am I noticing something that is ...
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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 ...
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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 ...
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