As I discussed here, the sensitivity of an option to one parameter can change as another parameter changes. A rough and ready check using CMI longevity data (nothing for CBD yet) bears out my intuition that as property values change, the longevity sensitivity of a no negative equity guarantee (NNEG) on a loan written on that property will also change.
The table below shows the cost of a NNEG for two different ages (60 and 70) and a range of loans to values from 10% to 50%. I assumed a loan rate of 6%, deferment rate 2.5%, current property value £100.
As is obvious from the table, the implied sensitivity to a longevity change of 1 year (crudely calculated as the 10 year change divided by 10) rises with LTV.
Since LTV is driven entirely by the property market (loan is fixed, value isn’t), it will rise as property prices fall, and so longevity risk increases in a bear market.
It follows that, if the capital requirement has been prudently estimated, i.e. if longevity risk has been incorporated into the calculation at all, then it will rise as property values fall. But that’s nasty. As property values fall, the capital available will also fall, hence the capital ratio (capital available divided by capital required) will be hit on both sides. The less capital you have, the more you need.
But not to worry, I am sure that the regulators knew what they were doing when they approved the capital regime for this product.
Have a good weekend.
| Age | |||
| LTV | 70 | 60 | Change/year |
| 10% | 4.35 | 24.03 | 1.97 |
| 20% | 13.69 | 46.52 | 3.28 |
| 30% | 22.31 | 60.19 | 3.79 |
| 40% | 29.30 | 69.01 | 3.97 |
| 50% | 34.83 | 75.09 | 4.03 |
Table: implied cost of NNEG for different ages and loans to values