Horizontal Slicing Method
Hi,
You put following comments for the horizontal slicing method:
Notice the horizontal method really only lends itself to calculating at entry ratios corresponding to known losses.
To calculate an "in-between" entry ratio insurance charge, form a trapezoid and add that area instead.
Fisher points out in practice there are usually sufficient losses to construct a Table M with intervals of 0.01 between rows
and that linear interpolation is usually accurate enough.
However, if I use the formula [Previous phi(r) + % over r X % change in r], it will give me all the phi(r) for in-between entry ratios. Those values are the same as calculated from vertical slicing method and also the linear interpolation at the same time. But it's equivalent as adding the area of a rectangle in stead of a trapezoid. You can see my calculation in the attached file.
Do you think I can do this way? Why the comment is necessary here?
Thank you,
CFX
Comments
Finally, I think the solution for question 3.7 in the source text (Page 107-110) explained what the authors mean about their warning. The issue is from if certain points are not used for the horizontal slicing method calculation (in the case, r = 0.25 and r = 0.75). Then, if we approximate something like r = 0.875 using r = 0.5 and r = 1.0 will not give the same number as vertical slicing method. However, if we use r = 0.75 and r = 1.0 to do the same thing, we will not have the issue. In our example, we used all the points but we just add some more, both methods will give the same results. Am I right?
Great question and comment thank you. Remember, a rectangle is a special case of a trapezoid where the two parallel sides have equal length.
Also recall the vertical slicing method gets the exact answer because it forces you to consider every possible entry ratio that you know. Whereas with the horizontal slicing method you're really picking a spacing for the entry ratios such as every 0.5 or 0.01 and constructing an approximation. This horizontal slicing example is perhaps misleading because it only used the known entry ratios. A more likely phrasing would be "use the horizontal slicing method with increments of 0.25 to build a Table M". In this case, if you don't in-fill with the known entry ratios (which are likely not increments of 0.25) then you get a poor approximation.
The Fisher Case study goes into this in more detail in steps 6 and 7.
You are right. After doing more other related topics, in this case, the case study, we can get more idea about certain questions. Yeah, the case study is a really good example as explanation! Thanks!