## Exponential Ornstein-Uhlenbeck process

Let’s consider parameter estimation for the following modification of Ornstein-Uhlenbeck process:

This model is simplification of Schwarz Model 1, one of Short-rate models

To find the explicit formula of the process, let’s apply Ito lemma to the following function

Calculating partial derivatives:

and finally by Ito lemma:

As and :

Therefore:

Thus this process might be used in Monte Carlo simulations as follows:

And process parameters can be estimated on as it is done for standard Ornstein-Uhlenbeck process here.

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Hi Paul,

Thank you for this great article.

I wonder what would be an ideal solution for the calibration of this process? I tried the method from your other link but got stuck at deciding the volatility sigma. As can be seen from the above equation, we have 0.5*sigma^2*dt and another one which is sigma*sqrt(dt). If we use OLS, would the constant (intercept) = 0.5*sigma^2 and sde = sigma*sqrt(dt)? Hence which one we use for estimating the sigma of the process?

Many thanks.

Kind regards,

Julie

Julie WongNovember 15, 2013 at 10:36

Hi Julie,

Sorry for the delay but the end of the year is always filled with a lot of task. I wrote a separate article about the calibration: http://wp.me/p1gkpt-cf

Hope it helps and it is not so late.

Regards,

Pavel

fxpaulNovember 20, 2013 at 13:06

[…] the previous article about process calibration we derived the following updating formula: Now we can rearrange equation’s parts as follows: […]

Estimation of Exponential Ornstein-Uhlenbeck process | FxPaulNovember 20, 2013 at 13:04