How do collateral payments work under a longevity swap?

The core reading under chapter 22 says "Collateral is calculated regularly and paid between insurer and reinsurer to reflect the value of the swap at any given date, i.e. the present value of the floating leg less the present value of the fixed leg."

1. When it says "between insurer and reinsurer" does this mean sometimes it is paid by the insurer (to the reinsurer), and at other times it is paid by the reinsurer (to the insurer)?

When is the collateral paid BY the insurer?

1. Is this when the the present value of floating payments exceed the present value of fixed payments?
2. Is the collateral amount paid equal to the difference between the present value of floating payments less the present value of fixed payments?

When is the collateral paid BY the reinsurer?

1. Is this when the the present value of fixed payments exceed the present value of floating payments?
2. Is the collateral amount paid equal to the difference between the present value of fixed payments less the present value of floating payments?

Would the collateral payment be 0?

1. Would the collateral payment be zero if the present value of floating payments equaled the present value of fixed payments?

I do not fully understand what a collateral is and how they operate under a longevity swap, so will appreciate if you can clarify the above and/or provide some examples.

 

Hi curiousactuary,

Some comments from me: hope it helps.

1. Whether the insurer or reinsurer posts collateral will depend on the difference between the value of fixed and floating legs (i.e. the value of the swap). An insurer would enter into a longevity swap to remove longevity risk: they would therefore be paying the fixed leg and receiving the variable leg. If PV fixed leg > PV floating leg, then the insurer would post collateral. If PV fixed leg < PV floating leg, the reinsurer would post collateral.

The collateral mitigates the counterparty risk.

When is the collateral paid BY the insurer?
1. Other way around
Rationale: When PV fixed leg > PV floating leg, the initial pricing assumed fewer deaths than is currently considered most likely. Consequently, the insurer is paying more ('fixed leg') than the current market pricing would imply if the longevity swap was transacted now.
2. Other way around but yes.


When is the collateral paid BY the reinsurer?
1. Other way around
2. Other way around but yes.

Would the collateral payment be 0?
Yes. The PV of floating leg would be priced to equal the PV fixed leg at contract inception.

In practice, the reinsurance agreement may require the insurer to post its fee to the reinsurer at time 0. But this is probably beyond the core reading, which I haven't read .

 

Thanks a lot for clearing this up Mogono.

Collateral definition
1. I just need to clarify what's meant by a collateral. When you say "insurer posts collateral", my understanding is that the insurer makes a payment to the reinsurer to cover the risk that the reinsurer may default on its floating series of payments - is that correct?

Why the insurer pays collateral to the reinsurer?
If the PV fixed leg > PV floating leg, then my interpretation is that the insurer is paying out more reinsurance premiums than the reinsurance claims that it is receiving - why then in this instance would the insurer then additionally pay out collateral to the reinsurer, especially when the insurer is already overpaying?

Why the reinsurer pays collateral to the insurer?
The same question applies vice versa.

The core reading says "
As a result of the transaction, the insurance company has fixed its future outgoings but has increased its counterparty risk, i.e. it is exposed to the risk that counterparty B does not honour its obligations. Equally, counterparty B is exposed to the risk that the insurance company defaults on its payments. Therefore, an important part of the swap is the collateral mechanism."

 

Collateral definition
Not quite. The reinsurer is exposed to the counterparty risk when PV fixed > PV floating. The effect of the collateral payment is to re-establish equilibrium: i.e. PV fixed = PV floating. Collateral arrangements settled on a 'net' basis will only need to cover the difference between the fixed and floating legs (and not the full amount).

Why the insurer pays collateral to the reinsurer?
Collateral is a mechanism to mitigate counterparty risk. Both parties want to be sure that the contract will be honoured at the point of settlement. It's a standard feature common in other contexts: e.g. interest rate / currency swaps, futures etc.

- Consider the case of an annuity writer concerned about longevity risk who takes out a longevity swap to mitigate the risk.
- In order to mitigate the longevity risk they would enter into a swap where they PAY (-) fixed and RECEIVE (+) floating payments
- Pairing this swap with their liabilities (-) under the annuity fixes the insurer's cash-flows. Algebraically: the floating payments (linked to longevity) paid out to annuitants cancels out with the floating payments received under the swap. The insurer's outflow is the fixed cash flows paid out under the swap. And the insurer is no longer exposed to the variable cash outflows linked to annuitant longevity.
- If levels of mortality amongst the reinsured annuitants is higher than originally priced, the insurer will continue (to remain) on the hook to pay the already agreed fixed cash flows but will now receive less from the reinsurer: why? because fewer annuity payments are now being expected to be paid.
- The reinsurer is the counterparty exposed to risk: they took the longevity risk (not the insurer), which would be unrewarded if the insurer didn't pay up.
-The reinsurer requires collateral to eliminate its counterparty exposure to the insurer.
-The collateral will be held until the claims are settled, which could be daily, monthly, quarterly etc.

Why the reinsurer pays collateral to the insurer?
The swap dynamics are similar to what i've described above. Two points to note:
1. The reinsurer will be taking the other side of the insurer's position. So they are PAYING floating and RECEIVING fixed payments.
2. The reinsurer is never on the hook to make payments to the u/l annuitants. So unlike for the insurer, the swap isn't being paired. And the reinsurer is now exposed to longevity risk (as a result of the swap).

I hope that helps to understand the Core reading.