Appendix B: FM Profiles

This section specifies the attributes and rules for the following list of Financial module profiles.

Profile description	calcrule_id
Do nothing (pass losses through)	100
deductible and limit	1
deductible with attachment, limit and share	2
franchise deductible and limit	3
deductible % TIV and limit	4
deductible and limit % loss	5
deductible % TIV	6
deductible, minimum and maximum deductible, with limit	7
deductible and minimum deductible, with limit	8
limit with deductible % limit	9
deductible and maximum deductible	10
deductible and minimum deductible	11
deductible	12
deductible, minimum and maximum deductible	13
limit only	14
deductible and limit % loss	15
deductible % loss	16
deductible % loss with attachment, limit and share	17
deductible % tiv with attachment, limit and share	18
deductible % loss with min and/or max deductible	19
reverse franchise deductible	20
deductible % tiv with min and max deductible	21
reinsurance % ceded, limit and % placed	22
reinsurance limit and % placed	23
reinsurance excess terms	24
reinsurance proportional terms	25
deductible % loss with min and/or max deductible and limit	26
% tiv trigger and % tiv step payout with limit	27
% tiv trigger and % loss step payout	28
% tiv trigger and % tiv step payout	29
% tiv trigger and % limit step payout	30
% tiv trigger and monetary amount step payout	31
monetary amount trigger and % loss step payout with limit	32
deductible % loss with limit	33
deductible with attachment and share	34
deductible % loss with min and/or max deductible and limit % loss	35
deductible with min and/or max deductible and limit % loss	36
% tiv trigger and % loss step payout with limit	37
conditional coverage payouts based on prior step payouts	38

calcrule_id	d1	d2	d3	a1	l1	sh1	sh2	sh3	st	ts	te	ps	pe	l2	sc1	sc2
100
1	x				x
2	x			x	x	x
3	x				x
4	x				x
5	x				x
6	x
7	x	x	x		x
8	x	x			x
9	x				x
10	x		x
11	x	x
12	x
13	x	x	x
14					x
15	x				x
16	x
17	x			x	x	x
18	x			x	x	x
19	x	x	x
20	x
21	x	x	x
22					x	x	x	x
23					x		x	x
24				x	x	x	x	x
25						x	x	x
26	x	x	x		x
27	x				x				x	x	x	x		x	x	x
28	x								x	x	x	x		x	x	x
29	x								x	x	x	x		x	x	x
30	x				x				x	x	x	x		x	x	x
31	x								x	x	x	x		x	x	x
32					x				x	x		x		x	x	x
33	x				x
34	x			x		x
35	x	x	x		x
36	x	x	x		x
37	x				x				x	x	x	x		x	x	x
38									x	x	x			x	x	x

The fields with an x are those which are required by the profile. The full names of the fields are as follows;

Short name	Profile field name
d1	deductible_1
d2	deductible_2
d3	deductible_3
a1	attachment_1
l1	limit_1
sh1	share_1
sh2	share_2
sh3	share_3
st	step_id
ts	trigger_start
te	trigger_end
ps	payout_start
pe	payout_end
l2	limit_2
sc1	scale_1
sc2	scale_2

An allocation rule can be assigned to each call of fmpy, which determines whether calculated losses should be back-allocated to the contributing items, and if so how. This is specified via the command line parameter -a.

The choices are as follows;

Allocrule description	allocrule_id
Don’t back-allocate losses (default if no parameter supplied)	0
Back allocate losses to items in proportion to input loss	1
Back-allocate losses to items in proportion to prior level loss	2
Back-allocate losses to items in proportion to prior level loss (reinsurance)	3

Effective deductibles

Often there are more than one hierarchal levels with deductibles, and there is a choice of methods of accumulation of deductibles through the hierarchy. Whenever a rule with a deductible is used in the loss calculation then it is accumulated through the calculation in an effective_deductible variable. The effective deductible is the smaller of the deductible amount and the loss.

All deductibles amounts calculated from the deductible_1 field are simply additive through the hierarchy.

Ay any level, the user can specify a calcrule using a minimum and/or maximum deductible which changes the way that effective deductibles are accumulated.

For a minimum deductible specified in calcrules using the deductible_2 field, the calculation increases the effective_deductible carried forward from the previous levels up to the minimum deductible if it is smaller.

For a maximum deductible specified in calcrules using the deductible_3 field, the calculation decreases the effective_deductible carried forward from the previous levels down to the maximum deductible if it is larger.

Adjustment of loss for prior level limits

Loss adjustments due to minimum and maximum deductibles may lead to breaching or falling short of prior level limits. For instance, an increase in loss due a policy maximum deductible being applied can lead to a breach of site limit that applied at the prior calculation level. Conversely, a decrease in loss due to policy minimum deductible can leave the loss falling short of a site limit applied at the prior calculation level. In these situations the prior level limits are carried through and reapplied in all calcrules that have minimum and/or maximum deductibles.

We introduce the following variables;

• over limit is the sum of the amount by which limits are exceeded at the prior level calculation (positive measure)

• under limit is the smaller of the effective deductible and sum of the amount by which losses fall short of limits at the prior level calculation (positive measure). It represents the amount by which the loss can be adjusted upwards due to the enforcement of a maximum deductible at the current level.

• loss delta is the amount by which the loss would change due to the enforcement of a minimum or maximum ignoring prior level limits (positive for loss increase and negative for loss decrease). The loss is adjusted by an amount up to the loss delta depending on the values carried in the under and over limit variables

Scenarios for under and over limit

The over and under limit variables are initialised when there exist prior level limits. The possible cases are;

Case	Under limit	Over limit	Meaning
1	0	0	All prior level losses are exactly at their limits
2	0	>0	Some prior level losses are over limit and none are under limit
3	>0	0	Some prior level losses are under limit and none are over limit
4	>0	>0	Some prior level losses are over limit and some are under limit

When the loss delta is positive;

• in cases 1 and 2 the loss is not adjusted upwards because the prior level losses are already at their limits. The loss delta is added to the carried over limit.

• in cases 3 and 4 the loss is adjusted upwards to a maximum of the under limit. Losses are therefore adjusted up to the prior level limits and any excess loss delta is added to the over limit variable. The loss increase is subtracted from the carried under limit.

When the loss delta is negative;

• in cases 1 and 2 the loss delta is added to the over limit until the over limit is zero and any excess loss delta is used to adjust the loss downwards. Losses that are over limit by more than the loss delta remain at their limits, and decrease only if the over limit is fully eroded by the loss delta.

• in cases 3 and 4 losses are adjusted down fully by the loss delta, or to zero if the loss delta is greater than the initial loss. The loss adjustment is added to the carried under limit.

Current calculation level limits may also apply and these are used to update the over limit and under limit measures to carry through to the next level.

Calcrules

In the following notation;

• x.loss is the input loss to the calculation

• x.effective_deductible is the input effective deductible to the calculation (where required)

• loss is the calculated loss

1. Deductible and limit

Attributes	Example
policytc_id	1
calcrule_id	1
deductible_1	50000
limit_1	900000

Calculation logic

loss = x.loss - deductible_1;
if (loss < 0) loss = 0;
if (loss > limit_1) loss = limit_1;

2. Deductible, attachment, limit and share

Attributes	Example
policytc_id	1
calcrule_id	2
deductible_1	70000
attachment_1	0
limit_1	1000000
share_1	0.1

Calculation logic

loss = x.loss - deductible_1
if (loss < 0) loss = 0;
if (loss > (attachment_1 + limit_1)) loss = limit_1;
	else loss = loss - attachment_1;
if (loss < 0) loss = 0;
loss = loss * share_1;

3. Franchise deductible and limit

Attributes	Example
policytc_id	1
calcrule_id	3
deductible_1	100000
limit_1	1000000

Calculation logic

if (x.loss < deductible_1) loss = 0;
	else loss = x.loss;
if (loss > limit_1) loss = limit_1;

5. Deductible and limit as a proportion of loss

Attributes	Example
policytc_id	1
calcrule_id	5
deductible_1	0.05
limit_1	0.3

Calculation logic

loss = x.loss - (x.loss * deductible_1);
if (loss > (x.loss * limit_1)) loss = x.loss * lim;

9. Limit with deductible as a proportion of limit

Attributes	Example
policytc_id	1
calcrule_id	9
deductible_1	0.05
limit_1	100000

Calculation logic

loss = x.loss - (deductible_1 * limit_1);
if (loss < 0) loss = 0;
if (loss > limit_1) loss = limit_1;

10. Maximum deductible

If the effective deductible carried forward from the previous level exceeds the maximum deductible, the effective deductible is decreased to the maximum deductible value

Attributes	Example
policytc_id	1
calcrule_id	10
deductible_3	40000

Calculation logic

if (x.effective_deductible > deductible_3) { 
	loss = x.loss + x.effective_deductible - deductible_3;
	if (loss < 0) loss = 0;
	}
else {
	loss = x.loss;
     }

11. Minimum deductible

If the effective deductible carried forward from the previous level is less than the minimum deductible, the deductible is increased to the total loss or the minimum deductible value, whichever is greater.

Attributes	Example
policytc_id	1
calcrule_id	11
deductible_2	70000

Calculation logic

if (x.effective_deductible < deductible_2) { 
	loss = x.loss + x.effective_deductible - deductible_2;
	if (loss < 0) loss = 0;
	}
else {
	loss = x.loss;
     }

12. Deductible only

Attributes	Example
policytc_id	1
calcrule_id	12
deductible_1	100000

Calculation logic

loss = x.loss - deductible_1;
if (loss < 0) loss = 0;

14. Limit only

Attributes	Example
policytc_id	1
calcrule_id	14
limit	100000

Calculation logic

loss = x.loss;
if (loss > limit_1) loss = limit_1;

15. Limit as a proportion of loss

Attributes	Example
policytc_id	1
calcrule_id	15
limit_1	0.3

Calculation logic

loss = x.loss * limit_1;

16. Deductible as a proportion of loss

Attributes	Example
policytc_id	1
calcrule_id	16
deductible_1	0.05

Calculation logic

loss = x.loss - (x.loss * deductible_1);
if (loss < 0) loss = 0;

Go to Appendix C Multi-peril model support

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