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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R code for Ornstein-Uhlenbeck process
Can any one help me with some R code to run Ornstein-Uhlenbeck process?
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Is there a standard method for quantifying mean-reversion for use in directional trading?
Assuming a directional strategy (no pairs or spread trades) is there a "standard" method for quantifying mean-reversion? Should auto-correlation, variance ratios, hurst exponent, or some other measure ...
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Categories of systematic trading strategies?
What are the main categories of systematic trading strategies (e.g. momentum, mean reversion), as might be considered by an index or fund-of-fund analyst?
Are there any common sub-strategies?
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How to build a mean reverting basket?
I have been playing with mean reverting pairs, but seems that most of the low hanging fruit (ie pairs) have been squeezed already. I would like to start with mean reverting baskets (>2 securities) in ...
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Does your Parkinson volatility ratio work as Taleb explained?
According to Dynamic Hedging: Managing Vanilla and Exotic Options (Taleb, 1997), the Parkison volatility estimator has several meaningful properties. It is defined
$$P=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\...
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Is a stationary process necessarily mean-reverting?
Intuitively, a stationary stochastic process needs to be mean-reverting. This should follow immediately from the definition of stationarity: the mean of the process needs to be constant over time, so ...
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Is trading mean reversion of small principal components of prices profitable?
Many have told me that it is a good idea to look at the third principal component (PC) of yield curve movements, as well as third and fourth PC of G10 currencies. They claim these PCs represent "...
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Modeling Long-Term Mean Reversion in Asset Returns
Fortunately, for obvious reasons, few applications require simulating asset returns over horizons in excess of 30 years.
Nevertheless, simulations over long horizons are sometimes conducted as part ...
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Calculating half life of mean reverting series with python
I am currently attempting to calculate the halflife of a mean reverting series using python programming language and the theory of the Ornstein–Uhlenbeck process.
I have a series which when plotted ...
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Option pricing and mean reversion
In different books one can find a formula for option pricing when we assume that $\ln(S)$ follows a mean reversion process
$$ dS_t/S_t=\kappa(\theta-\ln(S_t))dt+\sigma dZ$$
If we calculate an ...
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How to approximate the time to mean reversion for implied volatility
Given an option and its implied volatility, and also the mean value of the implied volatility over the last 30 days, if we find that the current IV is significantly (> 1 std dev.) away from the mean, ...
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Mean Reversion Time Frame
I am running a mean reversion strategy. I have question with regards to half-life; I have heard of OU process to determine the half-life but it's not giving me that kind of result.
Can anyone ...
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Threshold calculation for buying a mean-reverting asset
I am trying to figure-out an optimal policy for buying a unit when its price follows a mean-reverting price process (Ornstein–Uhlenbeck), when I have a finite time deadline for buying the unit.
I ...
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How can I estimate the Ornstein-Uhlenbeck paramters of some mean reverting data that I have on R?
I have mean reverting data (Difference of 2 stock prices, that I want to do pairs trading on). I want to simulate my own mean reverting data as similar as possible to the real data that I have.
The ...
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Mean reversion time estimation
I am new to mean reversion trading, and I would like to get some good references about how to estimate the time it takes to a mean reverting process to cross its long term mean.
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Does predictability in a VAR process imply mean reversion or momentum?
There seems to be some disagreement in the literature about this. Define predicability of a stationary series to be $\sigma^2_{t-1} / \sigma^2_t$
Finding mean reverting portfolios using canonical ...
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Consequence of negative mean reversion of hull white one factor model
I tried to calibrate the data for hull-white one-factor model. Sometimes, I get negative estimate of mean reversion factor after the calibration process. When I plug the negative mean reversion factor ...
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Simple mean reversion strategy portfolio construction
I had a quick idea I wanted to test, but am not sure of the correct way to size bets. Basically, I think that for a given index (say S&P), I want to be long under performers and short over ...
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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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What is the probability of ruin of a Geometric Ornstein-Uhlenbeck process?
I would like to calculate the probability of ruin (or, default), i.e.
$$\text{Pr}(\tau<T),$$
where $\tau$ is the default time and $X_t$ follows the Geometric Ornstein-Uhlenbeck (O-U) process
$$...
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How to trade the Ornstein-Uhlenbeck process?
My question comes from this paper, which is a short version of Avellaneda's paper The picture bellow provides a summary of the equations.
Do I understand correctly that in order to trade OU process I ...
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The meaning of Ornstein-Uhlenbeck parameters
I am trying to understand theOrnstein-Uhlenbeck process
$dX_t = \kappa(\theta-X_t)dt + \sigma dW_t$
my question is what is the meaning of the parameters?
and assuming that we know those parameters ...
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Does mean reverting imply mean stationary?
If I have a time series that exhibits mean reverting properties, does it necessarily mean that the time series is mean stationary?
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How are momentum and reversion long/short strategies dynamically combined in trading?
I'm trying to understand how to combine two strategies dynamically in trading: one mean-reversion and the other momentum.
One way (also the simplest one) of doing this is by scaling/normalizing ...
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Why is the mean time-dependent in the Hull-White interest rate model?
In the Vasicek interest-rate model, the interest rate reverts to a constant mean. This makes sense to me. In my conception, the mean ought to be time-invariant, since interest rates don't follow an ...
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What is the probability that a OU process hits an upper barrier U before a lower barrier L?
What is the probability that the arithmetic OU process $dx_t= \theta(\mu-x_t)dt+\sigma dW_t$ hits barrier $U$ before hitting barrier $L$ when $L<x_0<U$ ?
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Mean Crossing for Ornstein-Uhlenbeck
Suppose we have classic Ornstein-Uhlenbeck process. How can we calculate expected number (and variance too) of crossing mean value over the certain period of time?
Say, if we have discrete OU process ...
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Why is OU process stationary?
The mean and variance of Ornstein–Uhlenbeck (OU) process have time dependence (exponentially decay in time). So they are not constant in time. How can it to be stationary?
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Are there alternatives to the Box-Tiao decomposition in identifying mean reverting portfolios?
As documented in this paper,
(Identifying Small Mean Reverting Portfolios,
by Alexandre d’Aspremont, February 26, 2008)
Box-Tiao decomposition (a way to decompose multiple time series into components ...
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How to get set the theta function in the Hull-White model to replicate the current yield curve
I want to calibrate the HW one factor model to current market data. How do I set the function $\theta(t)$ in
$$
\mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t)
$$
to ...
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Speed of mean reversion of an interest rate model
I would like to have a bit more of intuition about the concept of "speed of mean reversion" for an interest rate model, e.g. Vasicek or CIR. In particular, is a negative speed of mean reversion ...
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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 ...
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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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Tests for Mean Reversion in a Portfolio Rebalancing
On a single time series one can run a Dickey-Fuller test to determine if the asset is mean reverting or at least has been mean reverting during your sample.
Is there a way to test for mean-reversion ...
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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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What is the effect of mean-reversion on an upper barrier knock-out call option?
Consider a mean-reverting normal model for an underlying
$dX^{(1)}_t=-\kappa X^{(1)}_tdt+\sigma^{(1)} dW^{(1)}_t$,
for fixed time-independent constants, $\kappa$ (mean-reversion) and $\sigma^{(1)}$ (...
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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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What is a stochastic processes which reasonably captures commodity price dynamics?
What stochastic processes (and corresponding probability distributions) empirically capture spot/forward commodity prices and forward term structures?
Background
I want to use discounted cash flow ...
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How to estimate parameters for 2 correlated Ornstein-Uhlenbeck processes with maximum likelihood?
I would like to use maximum likelihood to estimate the parameters of two correlated Ornstein-Uhlenbeck processes from empirical data.
Do you have any good references for this? If you have any hints ...
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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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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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What is the covariance of two correlated Ornstein-Uhlenbeck processes?
What is the covariance of two correlated Ornstein-Uhlenbeck processes? I was trying correlation(1,2)*Var1^(1/2)*Var2^(1/2), but I am not sure! I took Var1=(sigma1^2/(2*speedofmeanreversion1))*(1-exp(-...
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Entry and exit points for very short mean-reverting timeseries
I have a model specifying a cointegration relationship on a number of transaction-level timeseries.
I would like to specify entry and exit points for trades where these points ideally would be just ...
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Statistical significance of a pair trading strategy
How can I test the significance of a pair trading strategy, i.e. that the H0 is "The strategy has no predicting power".
I was considering to use the technique in Evidence Based Technical Analysis ...
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Estimating mean reversion
I've read in some places that mean reversion parameters for a rates model, eg Hull White, can be estimated directly from the current yield curve. However I've not been able to find anything more on ...
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Electric power price parameter estimation
currently I am working through the paper of Tino Kluge "Pricing Swing Options and other Electricity Derivatives" to get a better understanding about the power markets.
The author establishes methods ...
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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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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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Position sizing for a mean reversion strategy
I have a model that returns z scores for a mean reversion strategy where z score is the current price minus average and divided by vol.
At the moment, positions are sized inverse linear to the z ...
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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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