Guaranteed payments

Life Insurance Products Valuation in R

Roel Verbelen, Ph.D.

Statistician, Finity Consulting

Guaranteed payments

Additional flexibility: life annuities with a guaranteed period.
A typical contract:
- Initially: $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ benefits are paid regardless of whether the annuitant is alive or not.
- Afterwards: $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ benefits are paid conditional on survival.

Mr. Incredible's prize!

Mr. Incredible is 35 years old.

He won a special prize: a life annuity of 10,000 EUR each year for life!

The first payment starts at the end of the first year. Moreover, the first 10 payments are guaranteed.

Can you calculate the value of his prize?

Mr. Incredible's prize in R

He is 35-years-old, living in Belgium, year 2013.
Interest rate is 3%.

Survival probabilities of (35)

# Survival probabilities of (35)
kpx <- c(1, cumprod(px[(35 + 1):length(px)]))

Discount factors

# Discount factors 
discount_factors <- (1 + 0.03) ^ - (0:(length(kpx) - 1))

Mr. Incredible’s prize pictured

# Benefits guaranteed
benefits_guaranteed <- c(0, rep(10^4, 10), rep(0, length(kpx) - 11))

# Benefits nonguaranteed
benefits_nonguaranteed <- c(rep(0, 11), rep(10^4, length(kpx) - 11))

# PV of the guaranteed annuity
sum(benefits_guaranteed * discount_factors)

85302.03

# EPV of the nonguaranteed life annuity
sum(benefits_nonguaranteed * discount_factors * kpx)

149675.3

# PV of the guaranteed annuity + EPV of the nonguaranteed annuity
sum(benefits_guaranteed * discount_factors) + sum(benefits_nonguaranteed * discount_factors * kpx)

234977.3

Let's practice!

Life Insurance Products Valuation in R