All Questions
Tagged with mean-reversion stochastic-processes
19
questions
12
votes
4
answers
12k
views
Is a stationary process necessarily mean-reverting?
Intuitively, a stationary stochastic process needs to be mean-reverting. This should follow immediately from the definition of stationarity: the mean of the process needs to be constant over time, so ...
9
votes
5
answers
2k
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 ...
6
votes
0
answers
3k
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 I ...
5
votes
1
answer
762
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 ...
5
votes
2
answers
2k
views
Why is OU process stationary?
The mean and variance of Ornstein–Uhlenbeck (OU) process have time dependence (exponentially decay in time). So they are not constant in time. How can it to be stationary?
4
votes
1
answer
17k
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 ...
4
votes
1
answer
767
views
What is a stochastic processes which reasonably captures commodity price dynamics?
What stochastic processes (and corresponding probability distributions) empirically capture spot/forward commodity prices and forward term structures?
Background
I want to use discounted cash flow ...
3
votes
3
answers
2k
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 ...
2
votes
1
answer
327
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
0
answers
54
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 ...
1
vote
2
answers
2k
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+\...
1
vote
1
answer
1k
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 (...
1
vote
1
answer
559
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 ...
1
vote
1
answer
313
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 ...
1
vote
1
answer
316
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 ...