Market consistent valuation of SII technical provisions is sometimes explained with references to results of the theory of options/derivatives pricing, but
personally I struggle a bit to understand to what extent this theory is applicable to insurance liabilities. Chapter 18 gave me some insights, but I'm not sure if they're correct.
When we want to price an option which depends on the value of some underlying asset, we take the expected value of the payoff it generates, with respect to a martingale measure, and discount it using a risk free rate. This is based on the idea of replication.
When we move to insurance liabilities, we no longer deal with the market risk only. In most cases the emerging cash flows either depend only on insurance risks (mortality, lapse etc.) or on both insurance and market risks (e.g. unit-linked or WP policies).
In the first case, for SII we need to project future cash flows using real-world probabilities, and discount using risk free rates of interest. Then add the risk margin on top. Does this approach basically assume that these projected cash flows are treated as FIXED for the replication argument to be applied? (ie find an asset to match the CFs in all possible states, but because our cash flows are treated as fixed, we are basically limited to an asset that's guaranteed to earn the risk free rate). And that the market value of the non-market risks is reflected seperately in the risk margin?
And in the second case (i'm assuming a simple case with no options/gtees), to project benefits or charges directly linked to the value of some underlying assets, we'd additionally use a fact that in a risk-neutral valuation risky assets earn the risk free rate (as the expected return). So the unit fund or asset shares need to be projected using the risk free rates of return.
I think the key point I'd like to confirm here is whether there's little (or nothing) that can be borrowed from the theory of risk-neutral valuation to deal with the insurance risks (ie reflect in the price possible deviations from the best estimates). And that this is why the problem of placing a MCV on insurance liabilities is split into two parts: BEL and RM?
Thanks,
Mateusz
personally I struggle a bit to understand to what extent this theory is applicable to insurance liabilities. Chapter 18 gave me some insights, but I'm not sure if they're correct.
When we want to price an option which depends on the value of some underlying asset, we take the expected value of the payoff it generates, with respect to a martingale measure, and discount it using a risk free rate. This is based on the idea of replication.
When we move to insurance liabilities, we no longer deal with the market risk only. In most cases the emerging cash flows either depend only on insurance risks (mortality, lapse etc.) or on both insurance and market risks (e.g. unit-linked or WP policies).
In the first case, for SII we need to project future cash flows using real-world probabilities, and discount using risk free rates of interest. Then add the risk margin on top. Does this approach basically assume that these projected cash flows are treated as FIXED for the replication argument to be applied? (ie find an asset to match the CFs in all possible states, but because our cash flows are treated as fixed, we are basically limited to an asset that's guaranteed to earn the risk free rate). And that the market value of the non-market risks is reflected seperately in the risk margin?
And in the second case (i'm assuming a simple case with no options/gtees), to project benefits or charges directly linked to the value of some underlying assets, we'd additionally use a fact that in a risk-neutral valuation risky assets earn the risk free rate (as the expected return). So the unit fund or asset shares need to be projected using the risk free rates of return.
I think the key point I'd like to confirm here is whether there's little (or nothing) that can be borrowed from the theory of risk-neutral valuation to deal with the insurance risks (ie reflect in the price possible deviations from the best estimates). And that this is why the problem of placing a MCV on insurance liabilities is split into two parts: BEL and RM?
Thanks,
Mateusz