BEL calculation

[prachi]

Hello - Could you please help me with below queries:

Chapter 11 (Que 11.6 - Best estimate liability determination for unit linked contract - under SII)
The solution says that non-unit related liabilities are calculated by discounting the projected non-unit cashflows. I understand that

To calculate the charges (to be included in non unit cashflows), the unit fund is also required to be projected. These unit funds growth projection will be based on risk free rate, since we are following market consistent valuation under SII.

To calculate cost of maturity guarantees (which is the difference between the guaranteed payout and Unit linked fund value, subject to max 0), the stochastic model could be used.
- This will again involve projecting the unit fund but with the "investment return" assumption as a stochastic variable.
- This is calibrated using "risk neutral" approach i.e., using risk free rates (as we are using market consistent basis under SII).
- Additionally, a volatility assumption is also added to these "investment return" projection which will depend on the funds chosen by policyholder.
- Thousands of simulation would run and for each simulation, the projected unit funds will be compared to guaranteed payouts and the difference between them ( i.e., the maximum (guaranteed benefits-unit funds, 0)) is discounted using risk free rate ( using the risk free rate as generated for that simulation).
- The average of these discounted values will give the best estimate value for cost of guarantee.

Is my understanding correct? If yes, then I am confused that
1. why the volatility assumptions are allowed in unit fund ( for cost of guarantee calculation purpose)? Won't it be same thing as saying the units funds are allowed to be projected based on expected return on invested assets i.e., we are deviating from market consistent valuation which essentially depicts that we should use only risk free rates?
2. Why volatility assumptions are not used for calculation of charges ?


Chapter 14 (Page 11 extract says that : "The use of market-consistent techniques ensures that market and credit risks – the risks that cashflows will vary with interest rates, stock market movements, volatilities, credit spreads and defaults – otherwise known as non-diversifiable or systematic risks, are appropriately allowed for within the market value of the liabilities." )
I am again not able to understand "volatilities" here. Could you please help me with this?

 

[Em Francis]

Hi
I have tried to answer your queries below:

Hello - Could you please help me with below queries:

Chapter 11 (Que 11.6 - Best estimate liability determination for unit linked contract - under SII)
The solution says that non-unit related liabilities are calculated by discounting the projected non-unit cashflows. I understand that

To calculate the charges (to be included in non unit cashflows), the unit fund is also required to be projected. These unit funds growth projection will be based on risk free rate, since we are following market consistent valuation under SII.

To calculate cost of maturity guarantees (which is the difference between the guaranteed payout and Unit linked fund value, subject to max 0), the stochastic model could be used.
- This will again involve projecting the unit fund but with the "investment return" assumption as a stochastic variable.
- This is calibrated using "risk neutral" approach i.e., using risk free rates (as we are using market consistent basis under SII).
- Additionally, a volatility assumption is also added to these "investment return" projection which will depend on the funds chosen by policyholder.
- Thousands of simulation would run and for each simulation, the projected unit funds will be compared to guaranteed payouts and the difference between them ( i.e., the maximum (guaranteed benefits-unit funds, 0)) is discounted using risk free rate ( using the risk free rate as generated for that simulation).
- The average of these discounted values will give the best estimate value for cost of guarantee.

Is my understanding correct? If yes, then I am confused that
1. why the volatility assumptions are allowed in unit fund ( for cost of guarantee calculation purpose)? Won't it be same thing as saying the units funds are allowed to be projected based on expected return on invested assets i.e., we are deviating from market consistent valuation which essentially depicts that we should use only risk free rates?

This is still market consistent as the model parameters are calibrated to observed market values. The expected return should be consistent with the relevant EIOPA Solvency II risk-free yield curve but then as long as the volatility of investment returns (around that expected value) is market consistent, ie implied from the price of traded derivatives on appropriate assets, then the valuation is market consistent.

2. Why volatility assumptions are not used for calculation of charges ?

As noted above they can be.

Chapter 14 (Page 11 extract says that : "The use of market-consistent techniques ensures that market and credit risks – the risks that cashflows will vary with interest rates, stock market movements, volatilities, credit spreads and defaults – otherwise known as non-diversifiable or systematic risks, are appropriately allowed for within the market value of the liabilities." )
I am again not able to understand "volatilities" here. Could you please help me with this?

Think of it as being the spread around the expected value which can be implied from the price of traded derivatives using option pricing techniques. ie back-solving Black Scholes.

 

[prachi]

This is still market consistent as the model parameters are calibrated to observed market values. The expected return should be consistent with the relevant EIOPA Solvency II risk-free yield curve but then as long as the volatility of investment returns (around that expected value) is market consistent, ie implied from the price of traded derivatives on appropriate assets, then the valuation is market consistent

Thank you so much for the reply It is extremely helpful, but apologies, I have some further follow up queries:
1. So, while calculating the Liabilities for unit linked products, is it a choice to adjust the "investment return" by allowing for the asset volatilities or the companies under SII will usually follow this approach?
Apologies, but i was under the impression that for market consistent its just risk free rate, therefore these additional question coming in my mind.

2. The discounting will still be done on only risk free rates, right?

 

[Em Francis]

Thank you so much for the reply It is extremely helpful, but apologies, I have some further follow up queries:
1. So, while calculating the Liabilities for unit linked products, is it a choice to adjust the "investment return" by allowing for the asset volatilities or the companies under SII will usually follow this approach?

Under Solvency II liabilities should be valued using a market-consistent valuation method. And using a risk-neutral valuation (discounting at the risk-free rate) is just a convenient method for doing so. Other market-consistent methods include the use of stochastic deflators which can be quite messy and complex.

And if a risk neutral valuation is chosen, then this would involve calibrating the model so that the assets have been assigned volatility parameters consistent with current market pricing (eg implied volatility) but their mean investment returns all equal the risk-free rate.

Apologies, but i was under the impression that for market consistent its just risk free rate, therefore these additional question coming in my mind.
2. The discounting will still be done on only risk free rates, right?

Yes, under a risk neutral valuation, the risk-free interest rate is also used to discount the future liability cashflows.

 

[prachi]

Very helpful, thank you so much for your time and appreciate your quick response.

 

[prachi]

Hi,

I have another doubt on this topic. So while doing ALM, a separate assets and liabilities projection models are used.
For liability projection, we consider all the decrements to project future premiums and outgoes.

But doesn't these decrements should also be allowed on asset side? Since any benefit paid out will reduce the asset and premiums will increase the assets?

If above is true, then the decrements allowed in both projection models are similar i.e., best estimate basis?

 

[Lindsay Smitherman]

The asset and liability projection models don't have to be separate. In fact, the same model would normally project forwards both asset values and liability values. As you recognise, this is because the projected cashflows are relevant to both. As stated in the Core Reading, trying to model the assets separately from the liabilities brings in the 'extra complication' from having to combine them and make sure that the cashflows are consistent between them - so would be an unusual approach to take.

The phrase 'asset model' typically refers to the model that is used to project future investment returns, likely stochastically (for ALM purposes). In other words, the model comprises the economic scenario generators across the relevant variables. So this might be a separate model from the main projection model, but the outputs from this asset model would feed into the latter.

Hope that makes more sense.

 

[prachi]

yes, thank you so much

 

[scr123]

"The best estimate liability (BEL) is the present value of expected future cashflows, discounted using a ‘risk-free’ yield curve (ie term-dependent rates)."

Does the BEL include premiums? (BEL cashflows = Benefits + Expenses - Premiums)?

 

[Em Francis]

"The best estimate liability (BEL) is the present value of expected future cashflows, discounted using a ‘risk-free’ yield curve (ie term-dependent rates)."

Does the BEL include premiums? (BEL cashflows = Benefits + Expenses - Premiums)?

Yes, future premiums only. So for SP business, the BEL wouldn't include the single premium.