Have a question about "How to estimate parameters for SDE with multiple Brownian Motions ?" Let's say $X_t$ follows the process: $dX_t=\mu dt+\sigma_1 dW_t^1 + \sigma_2 dW_t^2 $

I think I've checked Sim.DiffProc for R and SDE Toolbox for MATLAB. Could someone lead me on this matter please ? Thanks for your kind attention.


Thought to add this as a comment, but it appears too long.

Your question does not appear complete, that is, the rationale for using two Brownian motions is not clear. Note that \begin{align*} dX_t &= \mu dt + \sigma_1 dW^1_t + \sigma_2 dW^2_t \\ &=\mu dt + \sqrt{\sigma_1^2 + \sigma_2^2 + 2 \rho \sigma_1\sigma_2}\frac{\sigma_1 dW^1_t + \sigma_2 dW^2_t}{\sqrt{\sigma_1^2 + \sigma_2^2 + 2 \rho \sigma_1\sigma_2}}\\ &= \mu dt + \sigma dW_t, \end{align*} where $\sigma = \sqrt{\sigma_1^2 + \sigma_2^2 + 2 \rho \sigma_1\sigma_2}$ and $\Big\{W_t = \frac{\sigma_1 dW^1_t + \sigma_2 dW^2_t}{\sqrt{\sigma_1^2 + \sigma_2^2 + 2 \rho \sigma_1\sigma_2}}, \, t \ge0\Big\}$ is a standard Brownian. That is, $X_t$ is completely described by a one factor model.

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  • $\begingroup$ Thank you for your answers. Actually what I’m trying to do is implement marker price of risk for multiple sources of risk. Could you please kindly go www3.ntu.edu.sg/home/achleon/FE6516/… on Page 47. Sources of risks are lets say GDP and interest rate and bonds are gdp-linkers. $\endgroup$ – TryingtobeQuant Oct 14 '19 at 8:10
  • $\begingroup$ That is a complete difference question: it is regarding the determination of the market price of risk premium rather than the estimation of the parameters. You may ask this as another question. $\endgroup$ – Gordon Oct 14 '19 at 16:23

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