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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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 ...
4
votes
1answer
156 views
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 ...
0
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1answer
95 views
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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1answer
122 views
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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1answer
106 views
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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0answers
149 views
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 ...
2
votes
1answer
239 views
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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0answers
64 views
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 ...
1
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1answer
137 views
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 ...
0
votes
1answer
325 views
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 (...
0
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1answer
159 views
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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0answers
229 views
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 ...
2
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0answers
43 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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0answers
69 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 ...
4
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0answers
101 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 ...
4
votes
3answers
540 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 ...
0
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1answer
141 views
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 ...
0
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1answer
113 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
121 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
247 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 ...
1
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1answer
128 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
167 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+ ...
3
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0answers
378 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 ...
2
votes
1answer
190 views
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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0answers
83 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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0answers
71 views
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2answers
452 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 ...
1
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0answers
35 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, ...
4
votes
1answer
745 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 ...
1
vote
1answer
519 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 ...
10
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1answer
485 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
votes
0answers
255 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
65 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
119 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 ...
6
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2answers
481 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
155 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
votes
0answers
289 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 ...
4
votes
1answer
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 ...
2
votes
0answers
283 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 ...
2
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3answers
637 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
163 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
votes
1answer
389 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
votes
1answer
455 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
votes
1answer
209 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
359 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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votes
5answers
1k 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
1k 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
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0answers
205 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
$$...
0
votes
1answer
577 views
Mean Reverting to its own variance?
Good morning all,
When trying to decipher some documentation I have come across this stochastic process which seems to me much like a Ornstein-Uhlenbeck (or Vasicek) process.
$$dX_t=-\kappa(X_t-\...
