# Questions tagged [ornstein-uhlenbeck]

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### Ornstein-Uhlnbeck Process with Jumps

I am trying to simulate an OU Process (Vasicek version) with jumps and I would like to derive the drift and diffusion term when jumps are incorporated, which will enable me to perform monte carlo ...
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### Diagonalization of Matrix question about Alvaro Cartea Algorithimic and High frequency trading

I'm currently reading the book "Algorithmic and High Frequency Trading" by Alvaro Cartea and 2 others. I encountered this equation and went down a rabbithole of verifying it. [some text ...
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### Modeling mean-reversion for different volatility regimes

Motivation: Half-life (HL) period shows how long it takes for a mean-reverting process to return halfway to its mean after a deviation. Most commonly, an Ornstein–Uhlenbeck (OU) process is applied to ...
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### How to calibrate an O-U process based on historical data?

Background: I have been working on my master thesis project for the last few months and gave the final presentation on the 2023-06-01. As a part of the master thesis project, I did a complete ...
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### Testing the fit of an Ornstein-Uhlenbeck process

I would like to check if a time-series follows an Ornstein-Uhlenbeck process defined by an SDE: $$dX_t - \lambda (\mu - X_t) dt = \sigma dW_t$$ where $\lambda > 0$ is the mean-reversion ...
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### Calibrating the Ornstein-Uhlenbeck process with an additional parameter

Firstly I find the spread between two cointegrated time-series $Y_t$ and $Z_t$ by finding the best slope parameter $\beta$ in the equation $spread_t = Y_t - \beta Z_t$ (via Cointegrated Dickey-Fuller ...
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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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### Ornstein–Uhlenbeck process – integration by parts

While deriving the solution for the stochastic differential equation that models the Ornstein–Uhlenbeck process, Paul Wilmott (Paul Wilmott on Quantitative Finance, chapter 4, page 87) performs the ...
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### Digital call under Ornstein-Uhlenbeck dynamics

I am trying to price a digital option with payoff $\mathbb{I}_{S_T>K}$, where $S_t$ follows the Ornstein-Uhlenbeck dynamics $\mathrm{d}S_t=rS_t\mathrm{d}t+\sigma\mathrm{d}W^{\mathbb{Q}}_t$ in the ...
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### Pairs trading by transforming two cointegrated series into a mean-reverting process?

I am slightly confused about the following. Let us assume I have two cointegrated time-series. I would like to model their 'cointegration' by a mean-reverting Ornstein-Uhlenbeck process since if they ...
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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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I would like to examine the impact of the volatility on the transaction costs (Bid-ask spread). In my case I would like to examine this for power prices. However, I don't have access to actual order ...
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### Vasicek model - Bond price and volatility

Why does the bond price under the Vasicek model increase as the rate volatility increases? What is the intuition behind this?
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### How to fix my Ornstein-Uhlenbeck parameter MLE in Python?

I am trying to fit time-series data into an Ornstein-Uhlenbeck process. Here is my code so far: ...
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### Is Ornstein–Uhlenbeck process the continuous-time correspondence of AR(1) process?

I see the AR(1) process (with $|\alpha| < 1$) can be written in the following way: $$x_{t+1} = \alpha x_t + \epsilon_t$$ $$\Delta x_t = - (1 - \alpha) x_t + \epsilon_t$$ which looks quite like the ...
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### Develop an option pricing equation by Ornstein Uhlenbeck process

I know that Black-Scholes equation is based that the Equity price has a Geometrical Brownian movement. Can I develop from the same principles( now with transaction cost) that Black Scholes is ...
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### Solution to a Geometric Ornstein Uhlenbeck Process $dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t$

I've been searching for the solution to the modified Ornstein-Uhlenbeck process \begin{equation*} dX_t = \kappa(\theta - X_t)dt + \sigma X_t dW_t \end{equation*} but it surprisingly hard to find. The ...
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### Modelling EUR/USD rate with Ornstein-Uhlenbeck model

I have a data set of daily EUR/USD rate for time period 2000-2018. My goal is to model future behaviour of this financial time series using Ornstein-Uhlenbeck model: d X_t = \alpha (\theta - X_t) ...
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### 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 ...
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