I have been asked to look to refactor some code.

There is a line shown below:

$\text{implied covariance} = -\frac{(\text{var}_1 - \text{var}_2 - \text{var}_3)} {2}$,

where $\text{var}_1$ is the implied variance of AUDUSD, $\text{var}_2$ is the implied variance of USDCAD and $\text{var}_3$ is the implied variance AUDCAD

I understand that this is a calculation of covariance between AUDCAD.

However I don't understand the $\text{var}_1 - \text{var}_2 - \text{var}_3$ line. I thought the covariance between two variables was the variance of the two variables multiplied together divided by $n-1$.


1 Answer 1


I think what you are effectively looking at is

$$\ \begin{align} \log(S_{AUDCAD})&=\log(S_{AUDUSD})\pm\log(S_{USDCAD})\\ \Rightarrow z&=x\pm y \end{align} $$ Thus,

$$ \sigma_z^2=\mathrm{E}\left(\left(x\pm y\right)^2\right)- [\mathrm{E}(x\pm y)]^2 =\sigma_x^2+\sigma_y^2\pm 2\sigma_{xy} $$ Hence, $$ \tag{1} \sigma_{xy}=\frac{\sigma_z^2-\sigma_x^2-\sigma_y^2}{\pm 2} $$

Does that work for you?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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