1
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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.

| improve this answer | |
$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.