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# 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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108 views

### When constructing a cointegrating series, does choosing the linear regression with the lowest ADF test statistic yield the optimal hedging ratio?

Multiple sources say that you should find the optimal hedging ratio between two stocks in a pairs trade by conducting 2 linear regressions (with each stock as the independent variable), and using ...
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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+ ...
74 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 ...
1k views

### 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 ...
85 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. ...
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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 ...
348 views

### If two price series are cointegrated but not correlated, how do I find the hedge ratio?

Mathematically, what is going on here?
47 views

### mean reversion model estimation - what method?

how can I estimate this model for mean reversion?
109 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 ...
175 views

### 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 ...
294 views

### 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 ...
32 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, ...
3k views

### 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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### 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 $\sigma^{(1)}$ (...
1k views

### 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 ...
777 views

### 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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### Co integration of diverging time series

I have 2 time-series datasets. I am trying to find co integration between them. Now the thing is they are negatively correlated. So if I want to look at the distance between them, would I be right in ...
354 views

### What causes poor returns in pair trading of very cointegrated securities?

I've been running some backtests of a pair trading strategy on 1 year worth of 5 min bars of two securities and I've noticed pretty poor returns, especially once transaction costs are taken into ...
230 views

### 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 $L<x_0<U$ ?
225 views

### Modeling the Stock Market [closed]

Hi I was wondering what is the model that best describes the price movement of the stock market? A Brownian motion Process with drift? An Ornstein Uhlenbeck_process? (where the long term mean is ...
2k views

### 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 ...
242 views

### How to transform Ornstein-Uhlenbeck parameters from hourly to daily?

I get the parameters (long-term mean, volatility, mean-reversion speed, correlation) of two correlated Ornstein-Uhlenbeck processes via a likelihood estimation from hourly data. If I want to transform ...
Trying to evaluate model for pairs trading. Consider classic formula: $\frac{dP}{P} = adt+b\frac{dQ}{Q}+dX$, where $P$ and $Q$ are stock prices, and $X$ is a mean reverting process (MRP) and $a$ is ...