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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Mean Reversion without Bollinger Band

What are the ways one can trade mean reversion apart from using Bollinger Bands?
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2 votes
1 answer
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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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How to calculate volatility with and without mean reversion?

How to model mean reversion in a stationary time series variable, Yt, using the following first-order autoregressive model: If the one-period conditional volatility of the change in Yt is denoted by ...
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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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Do currency exchange rates mean revert?

I am trying to understand to what extend holding stocks in a foreign currency (such as USD) in a developed country (such as the UK) over the long term (say, over 15 years) exposes one to currency risk....
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Computing the average deviation range in a mean reverting series

Given a mean reverting time series, what's the appropriate measure to use to compute the range it deviates by before reversion? Assuming normal distribution, taking standard deviations of the actual ...
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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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1 answer
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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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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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1 answer
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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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1 answer
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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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1 answer
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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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2 answers
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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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1 vote
1 answer
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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 ...
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2 votes
1 answer
198 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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4 votes
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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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2 votes
2 answers
513 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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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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4 votes
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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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1 vote
1 answer
635 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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13 votes
1 answer
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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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2 votes
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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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2 votes
0 answers
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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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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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6 votes
2 answers
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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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1 vote
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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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9 votes
1 answer
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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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3 votes
0 answers
351 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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4 votes
1 answer
3k 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 ...
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2 votes
0 answers
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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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2 votes
3 answers
712 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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1 vote
2 answers
190 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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