MORTALITY SWAP VALUATION PROCEDURE



VALUATION METHODOLOGY

  1. The aim is to structure and value an in-force custom mortality-swap to hedge against longevity risk by transforming unknown cohort cash-outflows into known cash-outflows over a specified period.
  2. Suppose we have a portfolio of N pensioners aged x, on which we pay V dollars at payment times before adjusting for cost inflation and we want to structure a mortality swap to hedge against longevity risk over the next T years.
  3. We calculate the average payment per pensioner by dividing V by N which we denote as AVP, this becomes our payment per surviving pensioner. If the cost inflation for escalating payments is set at an annual rate of h, the value of the avarage payment per surviving pensioner after i time-steps from now is calculated as AVP*(1+h)^(i/f), where f is payment frequency per year, * is the multiplication operator and ^ is the power operator.
  4. Our total cohort cashflow at time step i is -N*AVP*(1+h)^(i/f)*S(i) where S(i) is the realised survival index at time step i. We structure our mortality swap to give the following cash flow at time step i : N*AVP*(1+h)^(i/f)*(S(ri)-S(ti)), where S(ti) is the survival index value agreed at the outset, and S(ri) is the realised survival index at time step i for a life aged x at creation of the mortality swap for the chosen reference population. Our aggregate cash-flow at time step i is now: -N*AVP*(1+h)^(i/f)*S(i) + N*AVP*(1+h)^(i/f)*(S(ri)-S(ti))=N*AVP*(1+h)^(i/f)*(S(ri)-S(i)-S(ti)). If the reference population experience matches our cohort experience, that is, S(ri)=S(i), our aggregate cashflow becomes -N*AVP*(1+h)^(i/f)*S(ti), which is known in advance. In most cases S(ri) and S(i) do not match but are highly positively correlated such that the variance of N*AVP*(1+h)^(i/f)*(S(ri)-S(i)-S(ti)) is very low when compared with the variance of -N*AVP*(1+h)^(i/f)*S(i), thus significantly reducing longevity risk.
  5. To value the mortality swap, we simply assume that expected survival probabilities S(ri) are realised, and discount the future cash-flows to get the sum of their present values.
  6. Click the view-page-by-view-page instructions below to value the mortality swap.

Financial solutions home page

  1. Log into your account or if you are a new user, register your account and enable two factor authentication.
  2. Click on the [Mortality swap] button, this will take you to the Dynamic-text-blocks parameters page.

Dynamic text-blocks parameters page

  1. Select to enter flat or time-varying yield curve at indicated times.
  2. Select to use system-default survival indices or your own-custom reference population survival indices.
  3. Select to enter time-varying or flat payment(un-adjusted for cost-inflation) per surviving annuitant at coupon payment times.
  4. Select to either apply weight to system-default mortality tables to get actual cohort mortality tables or other actual cohort mortality experience. If you choose to weight system default tables, you will be asked to enter a weight value. This weight will be applied to the system mortality tables which are either the ELT15(Males), or ELT15(Females). The weight will be applied to the chosen system mortality rates at applicable ages to get actual corhort mortality tables. Some form of calibration may be needed to get the weight value. If for example, the weight value entered is 0.95 relative to the ELT15(Males) tables, 0.95 will be multiplied to the ELT15(Males) mortality rates to get actual cohort mortality rates. Since 0.95 is less than 1, it means actual mortality experience is lighter than reference table mortality experience. On the other hand, if the weight value after calibration turns out to be higher than 1, lets say 1.05, it means actual cohort mortality experience is heavier than the reference table mortality experience.
  5. Enter the original number of outstanding payment times at time of initial creation/structuring of the mortality swap.
  6. Enter the current number of outstanding payment times.
  7. Enter the time till next swap payments in years.
  8. Enter swap payment frequency per year.
  9. Enter the age of same-age annuitants at time of initial creation/structuring of the mortality swap.
  10. Enter the number of same-age annuitants at time of initial creation/structuring of the mortality swap.
  11. Click the submit button, and this will take you to the array populating page.

Array populating page

  1. Enter zero rates convertible coupon-payment-frequency times per year at indicated times.
  2. If prompted, enter survival indices agreed-at-the outset at indicated times.
  3. If prompted, enter expected actual cohort survival indices at indicated times.
  4. Enter payment per surviving annuitant(un-adjusted for cost inflation) at indicated payment times.
  5. Click the submit button, and this will take you to the Mortality swap valuation parameters page.

Mortality swap valuation parameters page

  1. If prompted, select to enter choice of sex for default mortality tables.
  2. Enter the name of reference entity.
  3. Select the name of currency of valuation from the drop-down list.
  4. If prompted, enter multiplier-factor(weight) applied to system-default mortality tables to get actual cohort expected mortality.
  5. Enter future annual cost-inflation rate assumption applied to payments. The cost inflation rate assumption can be used in two equivalent ways. As a simple example, suppose you structure a three year mortality swap that is supposed to match yearly payments per survivor of 1000 escalated by cost inflation rate of 2%. You can choose to enter flat payment per survivor of 1000, and inflation rate assumption of 0.02. The system will calculate payment per survivor for year 1, year 2, and year 3 payments as 1000*1.02, 1000*(1.02)^2, and 1000*(1.02)^3, which results in three consecutive inflation-adjusted yearly payments of 1020, 1040.4, and 1061.208. Alternatively you can choose to enter time-varying payments per survivor of 1020, 1040.4, and 1061.208 and set the inflation rate assumption to 0.0. The result will be the same. If after choosing three time varying payments per survivor of 1020, 1040.4, and 1061.208, you set the cost inflation rate assumption as 0.02, the system will calculate inflation adjusted payments per survivor as 1020*1.02, 1040.4*(1.02)^2, and 1061.208(1.02)^3. This will result in three consecutive payments per survivor of 1040.4, 1082.432, and 1126.162.
  6. Click the submit button and this will take you to the output display page.

Output display page

  1. You can view pricing model output together with input parameters you entered.
  2. At the bottom of the page you can click on the button to create database record for the current model output. This will take you to the create database record page where you should click on the create button to create the database record.
  3. After clicking on the create button to create the database record, you will be taken to the database records view page, where you can scroll vertically or horizontally to view database records including the one you just created.
  4. You can filter database records according to the currency of valuation using the filter box. You can click on the details link on the extreme right of a particular database record, this will take you to the particular database record details page.