Reserve risk, Stochastic Reserving and Capital Modelling

[Jun Wu]

Dear all

Hope you are well.

Just want to connect the concept of reserve risk with Stochastic Reserving and Capital Modelling chapters.

• My understanding is that reserve risk is the risk that our Best Estimate reserve comes out to be different to what is actually required, it is similar to a range of best estimate reserve?

• I also see the phrase variance of reserve/ultimate claims being mentioned in SP7, is that the same as reserve risk?

• Then, Stochastic reserving techniques such as bootstrapping an ODP is a way to estimate this reserve risk - ie it gives a distribution of reserve by simulation.

• Reserve risk is a component of capital model, and the capital charge for reserve risk is the difference between Best Estimate reserve and the reserve estimate at a chosen risk tolerance. What exactly does risk tolerance mean? I read about it being the VaR for example or is it the risk measure that I get confused with, but my understanding is that it can be anything such as the probability of the capital charge being enough to cover the short fall between Best Estimate reserve and the actual reserve required for 95% of the time. etc. ?

Please help me to understand this better, much much appreciated !

Many thanks
Best regards
Jun

 

[Ppan13]

Dear all

Hope you are well.

Just want to connect the concept of reserve risk with Stochastic Reserving and Capital Modelling chapters.

• My understanding is that reserve risk is the risk that our Best Estimate reserve comes out to be different to what is actually required, it is similar to a range of best estimate reserve?

• I also see the phrase variance of reserve/ultimate claims being mentioned in SP7, is that the same as reserve risk?

• Then, Stochastic reserving techniques such as bootstrapping an ODP is a way to estimate this reserve risk - ie it gives a distribution of reserve by simulation.

• Reserve risk is a component of capital model, and the capital charge for reserve risk is the difference between Best Estimate reserve and the reserve estimate at a chosen risk tolerance. What exactly does risk tolerance mean? I read about it being the VaR for example or is it the risk measure that I get confused with, but my understanding is that it can be anything such as the probability of the capital charge being enough to cover the short fall between Best Estimate reserve and the actual reserve required for 95% of the time. etc. ?

Please help me to understand this better, much much appreciated !

Many thanks
Best regards
Jun

Hi Jun,

Reserve risk is the risk that the level of reserves held by an insurer is inappropriate to the level and type of business written (e.g. such that it will not be adequate to meet the claims payable where under-reserved).

I’m not sure if this is just semantics, but rather than the range of best estimates, I think of it as the range AROUND the best estimate. i.e. a measure of the risk around the current reserves (with the run-off often defined over a certain time horizon, eg. 1 year). Part of the reason the reserves may end up being different to the best estimate will be down to process risk (e.g. incurred claims won’t be exactly as modelled/ estimated, due to many possible influencing factors). The estimation or modelling of reserve risk (e.g. using stochastic techniques as you mentioned) also introduces parameter risk into the reserve risk output.

The modelling of reserve risk will give you a risk profile or distribution, and the risk measure is chosen (e.g. VaR here) at some tolerance level (eg. 99.5%) . Other risk measures you could choose instead are standard deviation or Tail Value-at-Risk (TVar) , and you could specify other risk tolerances, e.g. 95% VaR, or "3.5 x Standard Dev", or 95% TVaR etc.

 

[Jun Wu]

Hi Jun,

Reserve risk is the risk that the level of reserves held by an insurer is inappropriate to the level and type of business written (e.g. such that it will not be adequate to meet the claims payable where under-reserved).

I’m not sure if this is just semantics, but rather than the range of best estimates, I think of it as the range AROUND the best estimate. i.e. a measure of the risk around the current reserves (with the run-off often defined over a certain time horizon, eg. 1 year). Part of the reason the reserves may end up being different to the best estimate will be down to process risk (e.g. incurred claims won’t be exactly as modelled/ estimated, due to many possible influencing factors). The estimation or modelling of reserve risk (e.g. using stochastic techniques as you mentioned) also introduces parameter risk into the reserve risk output.

The modelling of reserve risk will give you a risk profile or distribution, and the risk measure is chosen (e.g. VaR here) at some tolerance level (eg. 99.5%) . Other risk measures you could choose instead are standard deviation or Tail Value-at-Risk (TVar) , and you could specify other risk tolerances, e.g. 95% VaR, or "3.5 x Standard Dev", or 95% TVaR etc.

Thanks Ppan13! this is very helpful indeed!

I get reserve risk, variance of reserve, and range around BE reserve are all different concepts but related.

And CH16 are used to estimate the variance/mean and distribution of reserves.

On risk measure and tolerance level: for example, if we select 95% VaR, is it correct to say - we hold x amount of capital so that 95% of the time this capital is enough to cover the shortfall between actual liability and best estimate reserve?
I may be wrong about the use of VaR here, but I am trying to say we hold a capital amount to achieve the chosen risk measure and tolerance level.

Thank you!
Have a good weekend
Jun

 

[Aman Sehra]

Thanks Ppan13! this is very helpful indeed!

I get reserve risk, variance of reserve, and range around BE reserve are all different concepts but related.

And CH16 are used to estimate the variance/mean and distribution of reserves.

On risk measure and tolerance level: for example, if we select 95% VaR, is it correct to say - we hold x amount of capital so that 95% of the time this capital is enough to cover the shortfall between actual liability and best estimate reserve?
I may be wrong about the use of VaR here, but I am trying to say we hold a capital amount to achieve the chosen risk measure and tolerance level.

Thank you!
Have a good weekend
Jun

Hi Jun,

Value at risk is defined in the glossary. There is also a good overview in Chapter 20, Section 2.3 (steps in running a deterministic model). I hope this helps.

Thanks
Aman
Acted Tutor

 

[Ppan13]

....
On risk measure and tolerance level: for example, if we select 95% VaR, is it correct to say - we hold x amount of capital so that 95% of the time this capital is enough to cover the shortfall between actual liability and best estimate reserve?
I may be wrong about the use of VaR here, but I am trying to say we hold a capital amount to achieve the chosen risk measure and tolerance level.
...

Yeah, I think that's correct. By setting your risk measure and tolerance, you determine your capital requirement of “x” such that there is 95% probability that £“x” would be adequate to cover liabilities (over the specified time horizon e.g. over the next one year).

The core reading/ notes describes risk profile, risk measure and risk tolerance. In chapter “Capital modelling – assessment of capital for various risk types” , there is a section called “Core features of capital models”

The definition (in ActEd notes, not core reading) of 99.5% VaR was given in the early part of the previous chapter: “Capital Modelling- Methodologies” .

Another example of where VaR is applied is in the SCR (Solvency Capital Requirement) which is defined as "a Value at Risk measure based on a 99.5% confidence interval of the variation over one year of the amount of “basic own funds” [= assets minus liabilities]" ; So there is a 99.5% probability that the capital held at SCR level would be sufficient to cover liabilities. I don't think SCR is specifically covered in the SP7 syllabus though as it relates to Solvency II (regulatory capital requirements), but it shows you a typical way VaR is used/ expressed. I don't think SP7 mentions "basic own funds" (assets minus liabilities) but in the core reading paragraph about Risk Measure it does refer to the surplus on the balance sheet, so the concept is the basically the same (since the surplus is the 'assets less liabilities', which is = capital). Core reading on risk measure says "For example, we might set capital to achieve a selected probability that the balance sheet at the end of one year shows a surplus of no less than zero".

Have a good weekend, too!