Must admit it has been many years since I have done advanced calculations or anything remotely like it, so please bear with me. I have problem that I hope to get some help with. Say I have below dataset:
| Quarter | Exposure | Loss Given | Probability of | Estimated Loss | | | | Default (%) | Default (%) | | |-----------|------------|----------------|-------------------|-------------------| | Q1 | 100,000 | 3.0% | 5.0% | 150.0 | | Q2 | 150,000 | 2.8% | 5.5% | 231.0 |
Estimated Loss = Exposure x Loss Given Default x Probability of Default.
My problem now is, I would like to be able to explain the difference between Estimated Loss in Q2 and Q1, by explaining how much of the delta is due to the change in each parameter, or how much each parameter contributes of the change - if that makes sense?
Ideally I would like to be able to say something like below:
231 - 150 = 81, of which: +76 due to increase in Exposure -10 due to decrease in Loss Given Default +15 due to increase in Probability of Default
The reason behind showing it like this, is to make it more "understandable" for the reader who is not aware of the mechanics behind the numbers.
My initial thinking was to see what effect it had on Estimated Loss by changing only one parameter at a time; but I will miss some multiplier-effect, since the parameters are not independent.
Also if done this way - the order of how I show the change affects the outcome. Say I first change Exposure and see the result, next up LGD and lastly PD - then, because they are dependent, the effect is larger in PD than in Exposure - and other way around if I change the order. That was when I realised that I should probably have brushed up on my math skills.
1) Would it even be possible/make sense to explain the delta as above, where it can be determined how much each paramter contributes of the delta?
2) If it is possible; I assume that I need to do some sort of Partial Differential equation?
Thanks for you help :-)