1. The aim is to structure and value an in-force custom longevity bond to hedge against longevity risk by producing an income stream that closely mirrors outgo from our portfolio of annuitants for a specified number of years.
  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 longevity bond 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. Suppose we decide on structuring a longevity bond that pays mortality related coupons at a fixed nominal rate of r convertible f times a year. To set the notional principal P(i) at time step i from now that ensures payments cover our corhort payments under the assumption that they all survive(non-mortality related) we simply solve the following equation for P(i): P(i)*r/f = N*AVP*(1+h)^(i/f). The result is P(i) = (f/r)*N*AVP*(1+h)^(i/f).
  5. The P(i)'s set at the out-set are notional except for the terminal value of P(i) which is P(n). P(n) is the payable terminal principal. The notional principals at other time-steps are simply used to calculate the value of cohort payments. The cohort payment at time i is calculated as P(i)*S(i)*r/f where S(i) is the realised survival index at time step i for a life aged x at creation of the longevity bond.
  6. The value of the longevity bond is calculated by adding the total present value of mortality related cohort payments calculated under the assumption that expected survival probabilities of the reference population are realised to the present value of terminal principal.
  7. Although the valuation described in this application relates to pensioners, it can be applied to other life annuitants.
  8. Click the view-page-by-view-page instructions below to value the longevity bond.

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 [Longevity bond] 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 pensioner at coupon payment times.
  4. Enter the original number of outstanding coupons at time of initial creation/structuring of the longevity bond.
  5. Enter the current number of outstanding coupons.
  6. Enter pensioner age at time of initial creation/structuring of the longevity bond.
  7. Enter the time till next coupon payments in years.
  8. Enter coupon payment frequency per year.
  9. Enter the number of same-age pensioners at time of initial creation/structuring of the longevity bond.
  10. 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 at indicated times.
  3. Enter payment per surviving pensioner(un-adjusted for cost inflation) at indicated payment times.
  4. Click the submit button, and this will take you to the Longevity bond valuation parameters page.

Longevity bond valuation parameters page

  1. If prompted, select to enter choice of sex for default mortality tables.
  2. Enter the name of reference entities.
  3. Enter the name of currency of valuation.
  4. Enter the nominal coupon rate rate convertible coupon-payment-frequency times per year.
  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 longevity bond 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.