My project is to set a distribution loss of PNL in CHF into a distribution loss in USD. To do this I will need to have a distribution loss of the spot rate CHF/USD. I have simulated this distribution.
So have 2 distributions:
A: One is the simulated spot rate of USD/CHF
B: The other is the loss distribution of the PNL of my fund in CHF
I need to find out a way to multiply these 2 distributions in order have, as final result, the distribution loss of the PNL in USD. Since multiplication is not possible I chose convolution between both distributions.
In R I used the function "convolve. However, If I run
the result does not at all seems right to me, because the total number of entries is the sum of the entries of both distributions. Moreover, the results shows a Gaussian curve with only negative entries.
Could you please tell if I should apply convolution in the case? If no which method should I use to multiply both distributions?