# Estimating Market Price of Risk

I need help with estimating market price of risk. Assume money market account and two risky assets which exposed to same two sources of risks follow process:

$$dM(t)=rM(t)dt$$
$$dS_1(t)=S_1(t)(\mu_1dt+\sigma_{11 }dW_1(t)+\sigma_{12}dW_2(t))$$
$$dS_2(t)=S_2(t)(\mu_2dt+\sigma_{21 }dW_1(t)+\sigma_{22}dW_2(t))$$

and market price of risks defined as:

$$\theta_1 = \frac{\sigma_{22}(\mu_1-r)-\sigma_{12}(\mu_2-r)}{\sigma_{11}\sigma_{22}-\sigma_{12}\sigma_{21}}$$

and $$\theta_2$$ is derived in similar manner.

Assume $$S_1 and S_2$$ risky securities exposed to same uncertainty and their values are derived from those uncertainties. For example they are GDP linked derivatives/bonds and $$dW_1$$ comes from interest rate $$dW_2$$ comes from GDP.

My question is, given these two (or probably more) security prices and short rate and GDP data, how can I estimate parameters such as $$\sigma_{11}$$ $$\sigma_{12}$$ etc. or $$\theta_1$$ and $$\theta_2$$ themselves.