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Questions tagged [ornstein-uhlenbeck]

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3
votes
1answer
72 views

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 ...
5
votes
1answer
282 views

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) ...
2
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0answers
150 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 ...