Say for USDJPY and GBPUSD, I have the historic data and calc the volatility and correlation between these pairs.
Because GBPJPY = GBPUSD x USDJPY. Can I calculate the correlation for GBPJPY directly from these statistics, without having to calculate from the historic time series data?
I am not sure if its valid to use cosine rule, eg: Vol C ^ 2 = Vol A ^ 2 + Vol B ^ 2 - 2 * rho (A, B) * Vol A * Vol B Or if this is just for implied correlations.
As I tried it for some historic data and it didn't work.