Chapter 20: Reinsurance Pricing

[JL24]

Hello there, I have quite a few questions on this chapter, any opinions/explanations would be greatly appreciated

1. (Section 5, pg 31): The first bullet point of the last paragraph - 'meeting risk transfer criteria ...'
- Is this referring to the cedant's risk transfer criteria, or the reinsurer's (retrocession)?

2. (Section 6.1, pg 32): First paragraph after the bullet points - 'Note that the impact on pricing is likely to be greater where loadings based on volatility are used.'
- Would the limited reinstatements make the expected loss and standard deviation lower, reducing volatility; hence a lower loading would be needed?

3. (Section 6.1, pg 33): The approximation formula - 'the discount for paid reinstatements is estimated from...'
- Is the 'discount' here just referring to the 50% reinstatement rate? Because the formula seems more like applying the 50% rate with the aim of finding P' instead, though I can't see how P' is the 'discount'?

4. (Section 6.4, pg 36-37): Swing rates
- The example formula is using a 'loss load' as a factor for the first version and the 'swing'; as a factor for the second version.
a. From what I gathered, the 'loss load' is applied to aggregate recoveries, while the 'swing' is applied to each individual loss. Is this correct?
b. Does 'recoveries' above mean it is after deduction of the cedant's retention, while the 'loss' is just the ground-up loss?
c. Can I instead switch it around, i.e. apply the 'swing' on individual losses under the first version calculation; apply the 'loss load' on aggregate recoveries under the second version calculation?

5. (Section 6.5, pg 38): Loss ratio caps
a. The iterative pricing process - 'Reset the price with the maximum limit': Wouldn't this just be the same as the first price (without a limit)? Since I am obtaining the unlimited price, then using this price to work out the limit; wouldn't I just obtain the same price if I go the other way round (use the limit obtained to work out the price)?
b. Last paragraph - Under the unlimited price basis, wouldn't the cap already be so high that the likelihood of the cap being breached would be very low? The core reading says to assume the unlimited price if the probability of breach is very low, but wouldn't this just result in an excessively high premium being charged?

6. (Practice question 20.3 (iii), pg 56)
The insurer's net claims ratio (INCR) for the 'XOL Arrangement' and 'Quota Share' tables seem to be directly taking RR/RP.
- Isn't this the ceded (reinsurer's) loss ratio instead? Shouldn't it be
INCR = (Gross claims incurred adjusted by the 10% surplus - RR) / (Gross written premiums - RP)?
Using this equation, I was able to obtain the INCR for the final 'Quota share plus XOL together' table.

7. (Practice question 20.3 (iii), pg 57)
Smoothing: Both programmes smooth the net claims experience.
- Comparing the IGCR (pg 55, having 67% - 73%) and the INCR under QS/XLS (pg 56, having 68% to 75%), how has QS/XLS helped to smooth the experience? It seems to me that the ratio range has increased.

8. (Practice question 20.4 (i), pg 58)
- Why is the 'premium charged = risk premium / 0.8', instead of 'premium charged = risk premium * 1.2'?

9. (Practice question 20.4 (ii), pg 58): Bullet point 1
- Is this point just saying that if I take the 106k premium difference directly, the 20% loading would need to be changed (increased?) due to the premium being very small?

Thank you so much for reading to this point

 

[Aman Sehra]

Hi,

In response to your questions in the post above, please see below:
1) Generally speaking this would be cedant's risk transfer criteria, as they are the party who are transferring the risk.
2) Yes, you are along the right lines. Essentially, the use of limits means that the mean and standard deviation will be reduced, and so there is reduced volatility. In the pricing of the contract, since the volatility is reduced, the loadings required to calculate a price are likely to be reduced too.
3) P' is the reinstatement premium to be paid, if there is a loss which means a reinstatement is required. The difference here is that probabilities are being used to determine what the reinstatement premium will be based, based on the probability of there being a second (or at least 1 loss)
4a) Correct, but you can think of individual losses as 'aggregate losses'
4b) Yes I believe so
4c) There may be different ways to approach swing rating, that may not necessarily covered in the course notes (perhaps in industry other methods are used). In any case, you would be best placed to use the approach in the course notes, as this is what the examiners would be looking for, if this were to come up in the exam.
5a) Yes, but it is mentioned in the notes this is awkward to price! The main thing to recognize is that this is an iterative process, and would need to be done until the premium stabilizes
5b) Not quite, if the risk of the cap being breached is so very low (negligible) then the premium would be based on the expected losses. This may not be excessively high.
6) These are proportional reinsurance arrangements, so generally the proportion of premium is the same as the proportion of losses. There may be a few different ways to calculate and get the correct answer, but I suggest you follow the notes method, if this comes up in the exam.
7) The 'gross premium' on page 55 is not the incurred losses / gross premium - there is a note on page 55 as such. I suggest you look at the original question, and calculate gross loss ratios from there.
8) In the question we are told that there is a loading of 20% of the gross premium for brokerage etc. So, 20% of the gross premium consists of loadings. So, 80% of the gross premium is the risk premium. So: 0.8 x gross premium = risk premium. The calculation here is simply rearranging this.
9) This is saying that the 20% loading is quite a small number, and it is unlikely to be enough to compensate for contingencies (ie risk of there being more than 2 claims)

I hope this helps.

Aman
ActEd Tutor

 

[JL24]

Hi,

In response to your questions in the post above, please see below:
1) Generally speaking this would be cedant's risk transfer criteria, as they are the party who are transferring the risk.
2) Yes, you are along the right lines. Essentially, the use of limits means that the mean and standard deviation will be reduced, and so there is reduced volatility. In the pricing of the contract, since the volatility is reduced, the loadings required to calculate a price are likely to be reduced too.
3) P' is the reinstatement premium to be paid, if there is a loss which means a reinstatement is required. The difference here is that probabilities are being used to determine what the reinstatement premium will be based, based on the probability of there being a second (or at least 1 loss)
4a) Correct, but you can think of individual losses as 'aggregate losses'
4b) Yes I believe so
4c) There may be different ways to approach swing rating, that may not necessarily covered in the course notes (perhaps in industry other methods are used). In any case, you would be best placed to use the approach in the course notes, as this is what the examiners would be looking for, if this were to come up in the exam.
5a) Yes, but it is mentioned in the notes this is awkward to price! The main thing to recognize is that this is an iterative process, and would need to be done until the premium stabilizes
5b) Not quite, if the risk of the cap being breached is so very low (negligible) then the premium would be based on the expected losses. This may not be excessively high.
6) These are proportional reinsurance arrangements, so generally the proportion of premium is the same as the proportion of losses. There may be a few different ways to calculate and get the correct answer, but I suggest you follow the notes method, if this comes up in the exam.
7) The 'gross premium' on page 55 is not the incurred losses / gross premium - there is a note on page 55 as such. I suggest you look at the original question, and calculate gross loss ratios from there.
8) In the question we are told that there is a loading of 20% of the gross premium for brokerage etc. So, 20% of the gross premium consists of loadings. So, 80% of the gross premium is the risk premium. So: 0.8 x gross premium = risk premium. The calculation here is simply rearranging this.
9) This is saying that the 20% loading is quite a small number, and it is unlikely to be enough to compensate for contingencies (ie risk of there being more than 2 claims)

I hope this helps.

Aman
ActEd Tutor

Hello Aman,

Thank you so much for the explanation! I have 2 follow-up questions, if you don't mind:

5a) I understand that it is an iterative process, but I can't see how it can be iterative if the premium obtained in the 1st and 3rd steps are essentially the same? I feel like I am misunderstanding something in this part.

7) I have tried calculating the Gross Incurred Loss Ratio from the original question (without adjustment to remove the 10% surplus from the case estimates), and indeed the ratios range from 68% - 77% (bigger range than the net ratios under the QS/XLS arrangement).
However, isn't it still more consistent to use the Gross Incurred Loss Ratios (IGCR in pg 55) as the basis for comparison, since the INCR in pg 56 have removed the 10% surplus from the case estimates?

 

[Aman Sehra]

Hi there,

In response to your queries:

5a) For this part, simply knowing it is an iterative process, and the main steps, will be enough to get you through the exam - the detail and depth of how this works isn't required knowledge to get through the exam.
7) I am not sure I agree with this. We have been given gross written premium and gross incurred claims in the question - one divided by the other would give us a Gross Incurred Loss Ratio. Any further adjustments to this as a result of a reinsurance arrangement aren't strictly gross loss ratio.

I hope this helps.

Aman
ActEd Tutor

 

[JL24]

Hi there,

In response to your queries:

5a) For this part, simply knowing it is an iterative process, and the main steps, will be enough to get you through the exam - the detail and depth of how this works isn't required knowledge to get through the exam.
7) I am not sure I agree with this. We have been given gross written premium and gross incurred claims in the question - one divided by the other would give us a Gross Incurred Loss Ratio. Any further adjustments to this as a result of a reinsurance arrangement aren't strictly gross loss ratio.

I hope this helps.

Aman
ActEd Tutor

Thanks again Aman!