# 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?
94 views

### 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 ...
49 views

### 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 ...
209 views

### 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 ...
73 views

### 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 ...
1 vote
101 views

### 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 ...
72 views

### 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....
25 views

### 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 ...
277 views

### 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 ...
388 views

### 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 ...
353 views

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 ...
376 views

335 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 ...
71 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?
1 vote
136 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 ...
570 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 ...
1 vote
172 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 ...
2k 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 ...
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 ...
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 ...
321 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 ...