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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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 ...
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0answers
37 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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45 views
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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70 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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16 views
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 ...
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2answers
385 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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9 views
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 ...
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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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1answer
46 views
pair 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 ...
0
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1answer
87 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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1answer
79 views
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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2answers
79 views
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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1answer
89 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 ...
2
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1answer
143 views
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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0answers
191 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 ...
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1answer
119 views
Pairs Trading situation Spread changes
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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56 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 ...
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63 views
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2answers
317 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 ...
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0answers
34 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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1answer
482 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 ...
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1answer
262 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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202 views
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
$$P=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\...
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0answers
164 views
Position sizing for a mean reversion strategy
I have a model that returns z scores for a mean reversion strategy where z score is the current price minus average and divided by vol.
At the moment, positions are sized inverse linear to the z ...
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63 views
Effect of mean reverting Volatality in Black and Scholes? [closed]
Can someone please elaborate what would be the effect of a mean reverting volatility (instead of a constant volatility) in pricing options using BS ?
Also how would the greeks vary?
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0answers
95 views
Cointegration between daily time series and intraday time series
I am working with time series data of daily prices, and intraday prices. For simplicity sake I will refer to the daily time series as 'A' and 'B', and the intraday time series of the same instruments ...
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2answers
361 views
Does predictability in a VAR process imply mean reversion or momentum?
There seems to be some disagreement in the literature about this. Define predicability of a stationary series to be $\sigma^2_{t-1} / \sigma^2_t$
Finding mean reverting portfolios using canonical ...
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0answers
150 views
What does it mean that $\Phi$ is a mean-reversion factor?
Let $f$ be a variable which evolves according to the above. What does it mean to say that $\Phi$ is a mean-reversion factor?
I mean, I guess it means $f_{t+1} = (1-\Phi)f_t + \epsilon_{t+1}$ and so ...
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1answer
1k views
Option pricing and mean reversion
In different books one can find a formula for option pricing when we assume that $\ln(S)$ follows a mean reversion process
$$ dS_t/S_t=\kappa(\theta-\ln(S_t))dt+\sigma dZ$$
If we calculate an ...
2
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0answers
243 views
What is a stochastic processes which reasonably captures commodity price dynamics?
I ran into a stumbling block earlier when I tried to price stochastic annuities (see Asian options). This is actually technically an acturial problem, but is well adapted to the techniques of quant ...
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1answer
2k views
How to get set the theta function in the Hull-White model to replicate the current yield curve
I want to calibrate the HW one factor model to current market data. How do I set the function $\theta(t)$ in
$$
\mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t)
$$
to ...
2
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0answers
262 views
Frequency Arbitrage
We know that the volatility is lower when the sampling period is longer, for example $\sigma_{7days} < \sigma_{1day}$, Then I came across this strategy that I cannot quite understand how to exploit ...
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3answers
471 views
If two price series are cointegrated but not correlated, how do I find the hedge ratio?
Mathematically, what is going on here?
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2answers
147 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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1answer
352 views
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 ...
2
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1answer
362 views
R Mean Reversion Estimate on Funds
I am new to mean reversion, and I'd like to run an analysis on a fund (ts with monthly returns only) to see if mean reversion applies and if so, when it will happen.
Most of the examples I found ...
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1answer
200 views
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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0answers
338 views
How to calculate mean reversion values for Hull White tree calibration on MATLAB?
As part of a time series analysis, I'm writing a MATLAB program to create a Hull White tree, for the purpose of pricing a coupon-bearing bond.
While using the function hwvolspec (volatility ...
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5answers
881 views
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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2answers
753 views
Cointegration vs combination of returns
Hi Quantitative Finance,
I understand that there are a wealth of pairs trading models out there. Recently, it got me thinking as to why we go through the trouble to find cointegrated pairs while we ...
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0answers
184 views
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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1answer
505 views
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-\...
2
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0answers
669 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 ...
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1answer
593 views
Mean reversion formula in log normal or exponential form?
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 ...
2
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3answers
966 views
Cointegration pair trading - how to test a trading rule using Monte Carlo?
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 ...
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2answers
112 views
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 ...
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1answer
403 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 ...
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1answer
252 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$ ?
2
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1answer
232 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 ...
2
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0answers
386 views
cointegration strategy
If it can be proved that two time series
$$S_t^1=\alpha + \beta S_t^2 + \xi_t$$
representing stocks are correlated, with $\beta=-2$ and then are proved to be cointegrated,
how a portfolio should be ...
