1
$\begingroup$

If I know the price of $GBPUSD$ and $EURUSD$, I can retrive the $EURGBP$ price simple by $EURGBP = \frac{GBPUSD}{EURUSD}$.

Is there something equivalent to FX Volatility? Knowing the $\sigma_{GBPUSD}$, $\sigma_{EURUSD}$ and myabe $\rho[GBPUSD,EURUSD]$, is there a direct relationship or bounds to the value of $\sigma_{EURGBP}$?

I tried to think in terms of generic numeraie, like $USDX$ and $GBPX$, and take expectaions of the ratios, but I found no solution.

Any idea or clue would be helpful.

$\endgroup$
2
$\begingroup$

This is covered in the book "FX Derivatives Trader School" (and in other places, too, e.g. "The shape of things in a currency trio", a paper by Walter and Lopez, CS and FRB SF link).

$\endgroup$
2
  • $\begingroup$ @noob2 - thanks for adding the link! $\endgroup$
    – user42108
    Nov 19 '21 at 12:57
  • $\begingroup$ Thanks. It's simple a the volatility of a 'portfolio' invested 100% in both pairs. I should've seen that coming! $\endgroup$ Nov 23 '21 at 13:17

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.