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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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, ...
4
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1answer
182 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 ...
0
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1answer
51 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 ...
7
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0answers
106 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
$$P=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\...
2
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0answers
73 views
Position sizing for a mean reversion strategy
I have a model that returns z scores for a mean reversion strategy where z score is the current price minus average and divided by vol.
At the moment, positions are sized inverse linear to the z ...
2
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0answers
58 views
Effect of mean reverting Volatality in Black and Scholes? [closed]
Can someone please elaborate what would be the effect of a mean reverting volatility (instead of a constant volatility) in pricing options using BS ?
Also how would the greeks vary?
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0answers
66 views
Cointegration between daily time series and intraday time series
I am working with time series data of daily prices, and intraday prices. For simplicity sake I will refer to the daily time series as 'A' and 'B', and the intraday time series of the same instruments ...
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2answers
262 views
Does predictability in a VAR process imply mean reversion or momentum?
There seems to be some disagreement in the literature about this. Define predicability of a stationary series to be $\sigma^2_{t-1} / \sigma^2_t$
Finding mean reverting portfolios using canonical ...
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0answers
145 views
What does it mean that $\Phi$ is a mean-reversion factor?
Let $f$ be a variable which evolves according to the above. What does it mean to say that $\Phi$ is a mean-reversion factor?
I mean, I guess it means $f_{t+1} = (1-\Phi)f_t + \epsilon_{t+1}$ and so ...
8
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1answer
644 views
Option pricing and mean reversion
In different books one can find a formula for option pricing when we assume that $\ln(S)$ follows a mean reversion process
$$ dS_t/S_t=\kappa(\theta-\ln(S_t))dt+\sigma dZ$$
If we calculate an ...
2
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0answers
167 views
What is a stochastic processes which reasonably captures commodity price dynamics?
I ran into a stumbling block earlier when I tried to price stochastic annuities (see Asian options). This is actually technically an acturial problem, but is well adapted to the techniques of quant ...
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1answer
887 views
How to get set the theta function in the Hull-White model to replicate the current yield curve
I want to calibrate the HW one factor model to current market data. How do I set the function $\theta(t)$ in
$$
\mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t)
$$
to ...
2
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0answers
213 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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2answers
294 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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1answer
65 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 ...
5
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1answer
291 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
265 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 ...
3
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1answer
189 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
302 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 ...
7
votes
5answers
659 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
420 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 ...
6
votes
0answers
166 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),$$
where $\tau$ is the default time and $X_t$ follows the Geometric Ornstein-Uhlenbeck (O-U) process
$$...
0
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1answer
399 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
votes
0answers
548 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 ...
0
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1answer
469 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
votes
3answers
827 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 ...
1
vote
2answers
109 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 ...
1
vote
1answer
327 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 ...
5
votes
1answer
222 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
votes
1answer
215 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
votes
0answers
354 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 ...
5
votes
1answer
425 views
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 ...
2
votes
2answers
225 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 ...
4
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0answers
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 ...
4
votes
2answers
227 views
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 $\sigma^{(1)}$ (...
2
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1answer
1k views
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(-...
4
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1answer
696 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 ...
2
votes
1answer
503 views
Mean reversion and adjusted beta for pairs trading
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 ...
6
votes
1answer
6k views
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 ...
4
votes
1answer
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 ...
2
votes
0answers
57 views
How to optimize an arbitrage portfolio when taking into account different speeds of mean reversion?
In portfolio optimization, it is insufficient to just note the size of price deviation - that only tells the amount of profit if held to maturity. One also needs to take into account reversion speed - ...
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0answers
38 views
Quantitative Business Cycle Investing
Is there a major article or even better a comprehensive recent review article showing quantitative evidence for the existence of the business cycle and measuring the trending and mean reversion on ...
2
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0answers
195 views
Are there alternatives to the Box-Tiao decomposition in identifying mean reverting portfolios?
As documented in this paper, Box-Tiao decomposition (a way to decompose multiple time series into components with different speeds of mean reversion) can be used to identify mean reverting portfolios. ...
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1answer
1k views
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 "...
4
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1answer
259 views
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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1answer
70 views
Does it make sense to interpret autocorrelation and box test on 5 data points?
I am trying to see if after I trade a stock the price movements at 2, 5, 7, 10, 30 and 60 seconds after exhibit any autocorrelation. Below I have the returns from my trade price to the trade 2,5,7,10 ...
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2answers
744 views
Calibration of non-mean-reverting OU process
I'm looking for some reference on how to calibrate a non-mean-reverting Ornstein-Uhlenbeck process to historical data using MLE or OLS. The model has the following SDE:
$d\lambda(t)=a\lambda(t)dt+\...
3
votes
1answer
8k views
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 ...
6
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1answer
686 views
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.
3
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1answer
1k views
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 ...
