Hi - lots of questions! I will have a go at answering each in turn.
If the calculation is being done deterministically, then the cost of guarantees and options that it is included in the PVIF cashflows will only represent the intrinsic value. The EEV principles specify explicitly that the calculation also needs to take into account the time value of the option/guarantee, i.e. allowing for the possibility that it might bite in future even if it is not expected to bite on the base assumptions. This is therefore referred to separately. Yes, as you say, the time value would likely need to be determined using a stochastic model (or an equivalent technique which took into account the stochastic nature of the underlying variable, e.g. option pricing approach).
A non-market consistent embedded value uses the company's own best estimate assumptions for future investment return experience and a discount rate that would include a risk margin. A market consistent embedded value would (typically) use an expected future investment return equal to the risk-free rate, irrespective of the asset type (although there may be some allowance for a liquidity premium), and a discount rate that is also equal to the risk-free rate. So the "cost of required capital" for the non-market consistent EV will reflect the difference between rolling up the required capital at the assumed investment returns and discounting at the (normally higher) risk discount rate. For MCEV, there is no difference between the expected investment return and discount rate, so this approach would not give any lock-in cost of holding the required capital. Instead, the cost of having capital tied up in the business needs to be determined explicitly and will take into account the "frictional costs" that you mention. For a non-market consistent EV, the same frictional costs may also be taken into account - depending on the approach taken by that particular company (bearing in mind that there were no specific instructions under EEV as to how the "cost of required capital" element should be determined).
Yes, companies would either include explicit margins on their assumptions for mortality, expenses etc or would make allowance for these risks within the risk discount rate used (or a bit of both). Under MCEV, such assumptions would be best estimate and the risk-free rate is used as the discount rate; therefore there needs to be a separate allowance for these risks.
Under a liquidity crisis, the value of bonds can fall significantly and so the value of assets held by the insurance company will fall. The increased yield spread on these bonds reflects the increased (il)liquidity premium. If companies are permitted to take into account this liquidity premium in their market consistent calculations, this increases the risk-free rate that they can use for projecting the value of assets into the future, giving higher profits. These will be discounted by a higher rate, but the positive impact of having a higher earned investment return assumption (which applies to total assets held to back liabilities) is greater than the negative impact of having a higher discount rate (which applies only to the profits arising). So there will be some balance between lower asset values (in the free surplus component) and higher PVIF, and overall the MCEV should not change materially. If the liquidity premium had not been allowed, the MCEV would have fallen materially due to the fall in value of assets.
[If companies are allowed to take into account the liquidity premium in the calculation of their liabilities too (as may be the case under Solvency II, via matching/volatility adjustments - where permitted), then the liabilities will reduce in value as a result of being able to discount them using a higher rate. A reduction in liabilities will increase free surplus directly but will reduce PVIF as lower amounts of reserve will be released in the future projections. So there would be a similar effect overall.]
This justification is covered in Section 5 of Chapter 19 and you might also find it helpful to look at part (i) of Q2 in the April 2015 exam. Basically, PVIF is the present value of the release of future margins in reserves. So if reserves have been calculated on a best estimate basis (as under Solvency II: the BEL) there are no such future margins to release - hence no PVIF. There are some additional complexities around this, in relation to aspects such as liquidity premia, contract boundaries, with profits business, release of risk margin etc (as covered in the course notes) - but this is the underlying principle.
So if PVIF is zero (or close to zero), then the embedded value is simply free surplus + required capital - cost of holding required capital, which is broadly equivalent to Solvency II "own funds".
Hope that helps.
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