In France, the viager system is a special type of home sale. Under this type of agree
ment, the buyer agrees to pay the seller a down-payment and/or a whole life annuity in
exchange of the house ownership. Normally, the sellers will be allowed to stay in the sold
property for the rest of their lives. This essentially makes the price of the property a life
This contract is attractive to the house owners, normally retired people because it allows
them to extract values from their asset without making them homeless. For the buyers,
these type of properties are normally priced lower than the market price. Moreover, they
can gamble on the life of owners. If the owner passes away shortly after the sale, the
buyer would have acquire a house with low price. However, the whole life annuity in this
contract has to be payed until the seller pass away even if they out live the buyer. So it
would be unfortunate if the buyer buys the house from Jeanne Calment (Google it).
In this assignment, your group is required to design a simple viager sell and help to set
the payment level.
You are tasked to calculate the payment level for the whole life annuity for a specific
viager house sale and also assess the variance of the whole life annuity’s present value.
The default setting is as follows:
(a) This sale takes place in a city/town of your choice, so not necessarily France. Please
name the place in the first page of your report.
(b) The sale is solely paid for by a whole life annuity, so no down-payment. The specific
of the annuity will be given later but the actuarial present value of the annuity should
be equal to 80% of the market value of a typical apartment/house at the sale location.
(c) To keep the question simple, the effective annual interest rate used for discounting
is assume to be a constant and positive through the whole contract. You may pick
this interest rate yourself but you have to provide support/reasoning.
(d) Use the uniform distribution of deaths assumption for fractional age.
(e) In order to diversify the assignments, the problem settings will be personalized.
Details will be given later in this document.