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Question regarding definition of Ornstein-Uhlenbeck model code comment #4

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nhattan417 opened this issue Aug 28, 2024 · 4 comments

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@nhattan417
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Hi,
From the paper on PyMLE, the Ornstein-Uhlenbeck model is given by the SDE: $$dS_t=\kappa(\mu−S_t)dt+\sigma dW_t$$. However, in the documentation comment of the OU model code below, I see something different:

"""
Model for OU (ornstein-uhlenbeck):
Parameters: [kappa, mu, sigma]
dX(t) = mu(X,t)*dt + sigma(X,t)*dW_t
where:
mu(X,t) = kappa * (mu - X)
sigma(X,t) = sigma * X
"""

I believe line 17:
sigma(X,t) = sigma * X

should be re-written as:

        # sigma(X,t) = sigma

and the code relating to density and calculations should be adjusted accordingly?
Please correct me if I am wrong. Thank you.

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