Actuarial equivalence

Life Insurance Products Valuation in R

Katrien Antonio, Ph.D.

Professor, KU Leuven and University of Amsterdam

Actuarial equivalence of cash flow vectors

Establish an equivalence between two cash flow vectors.
Examples:
- mortgage: capital borrowed from the bank, and the series of mortgage payments;
- insurance product: benefits covered by the insurance, and the series of premium payments.

Mr. Incredible's new car

Car is worth $20 \, 000$ EUR;
Mr. Incredible's loan payment vector is $(0,K,K,K,K)$ with Present Value:

$$ \sum_{k=1}^4 K \cdot v(0,k) \, $$
Then, establish equivalence and solve for unknown $K$!

$$ 20\ 000 = \sum_{k=1}^4 K \cdot v(0,k). $$

Mr. Incredible's new car in R

# Define the discount factors
discount_factors <- (1 + 0.03) ^ - (0:4)

# Define the vector with the payments
payments <- c(0, rep(1, 4))

# Calculate the present value of the payments
PV_payment <- sum(payments * discount_factors)

# Calculate the yearly payment 
20000 / PV_payment

5380.541

Let's practice!

Life Insurance Products Valuation in R