# Tag Info

Accepted

### Calculating half life of mean reverting series with python

I found out what I was doing wrong - the OLS function was regressing with no intercept value - so I had to use the "add_constant" method to add an intercept term to the X series (z_lag) as follows: <...
• 351
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### How to get set the theta function in the Hull-White model to replicate the current yield curve

Concerning your first question, this depends on what curve, currency, etc. you are interested in. The general method for constructing yield curves is called bootstrapping which allows you to derive ...
• 8,059
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### Does your Parkinson volatility ratio work as Taleb explained?

I believe that Taleb made a mistake in his book. Several days ago I met the same question, and I came to read the original article of Parkinson(1980). After doing some simple math, I was aware that ...

### Option pricing and mean reversion

From the SDE \begin{align*} \frac{dS_t}{S_t}= k(\theta-\ln S_t) dt + \sigma dW_t, \end{align*} where $\{W_t,\, t\ge 0\}$ is a standard Brownian motion, we obtain that \begin{align*} d(e^{kt}\ln S_t) = ...
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### What causes poor returns in pair trading of very cointegrated securities?

A few possibilities - Trading costs kill your returns (often a problem for very highly correlated securities) Mean reversion of the cointegration spread is either very weak, or happens over periods ...
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### Modeling Long-Term Mean Reversion in Asset Returns

You could use the two factor model of Schwartz-Smith. It's a very standard model in commodities, where you observe this kind of long term mean reversion (where "long-term" is here around a year). It'...
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### Options Pricing and Mean Reversion

Joshi is correct. The no arbitrage argument implies that the stock price instantaneous return under the risk neutral measure is equal to the short rate, and the girsanov theorem implies that the ...
• 5,672
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### Interpretation and intuition behind half-life of a mean reverting process

In processes such as OU, it takes infinite time to revert to the mean completely. An unperturbed process starting at some point away from the mean asymptotes towards the mean without ever touching it. ...
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### Modeling Long-Term Mean Reversion in Asset Returns

One economic model you could look at is the Habit model of Campbell and Cochrane (1999). The basic idea is that as the consumption of the representative investor approaches the (appropriately defined) ...
• 468
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Accepted

### Does predictability in a VAR process imply mean reversion or momentum?

The point of confusion may be in thinking that a predictable price process is synonymous with a mean-reverting process while using the definitions in these papers, it's actually the opposite! In the ...
• 6,944
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• 6,628

### How to derive a pricing PDE for an asset that follows a mean-reverting process?

Let $\{r_t, \, t\ge 0\}$ be the interest rate process. For maturity $T$ and $0\le t \le T$, note that \begin{align*} V(S_t, t) = e^{\int_0^t r_s ds}\,\mathbb{E}\left(e^{-\int_0^T r_s ds}V(S_T, T) \...
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### Why is my mean-reversion half-life completely wrong?

I think the main problem is that, as @KurtG says, your example sine function exhibits strong momentum (albeit with reversals) and fitting an Ornstein-Uhlenbeck process to it results in strange ...

### Interpretation and intuition behind half-life of a mean reverting process

It might be helpful to consider an equivalent but different definition of the half life. Suppose we have a standard (zero-mean) OU process defined by $dx_t = -\theta x_t dt + \sigma dW_t$ (which is ...

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### Modeling Long-Term Mean Reversion in Asset Returns

Although I agree with jd8 answer, practical implementation issues may arise. Here I suggest a parsimonious engineering solution relying on economic intuition of Habit model of Campbell and Cochrane (...
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### R code for Ornstein-Uhlenbeck process

The Euler method is simple but it gives an approximate distribution. The method implemented below gives an exact distribution of $X_{t_i}$ and exact conditional distributions $(X_{t_j} \mid X_{t_i})$. ...

### Modeling Long-Term Mean Reversion in Asset Returns

I just wrote two papers on a related topic. Let us not use the log method right now as it was originally intended as an approximation from the time we used punch cards. You can, but we will come ...
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