valuer (version 1.1.2)

GMWB: Variable Annuity with GMWB guarantee

Description

Class for a VA product with Guaranteed Minimum Withdrawal Benefit (GMWB). A GMWB rider allows for periodic withdrawals from the policy account. Types of GMWB supported are withdrawals up to a fixed date independent of survival (Wa), withdrawals up to fixed date only if the insured is alive (Wb) or whole life withdrawals (Wc). It supports a simple state-dependent fee structure with a single barrier. See References for a description of variable annuities life insurance products, their guarantees and fee structures.

Usage

GMWB

Value

Object of R6Class

Format

R6Class object.

Methods

new

Constructor method with arguments:

payoff

payoff_GMWB object with the amount of the periodic withdrawal

t0

timeDate object with the issue date of the contract

t1

timeDate object with the end date of the contract

age

numeric positive scalar with the age of the policyholder

fee

constant_parameters object with the fee

barrier

numeric positive scalar with the state-dependent fee barrier

penalty

penalty_class object with the penalty

type

string with the GMWB contract type: it can be 'Wa' for withdrawals up to t1 independent of survival,'Wb' for withdrawals up to t1 only if the insured is alive, 'Wc' for whole life withdrawals.

freq

string with the frequency of withdrawals expressed in months (e.g. '12m' stands for yearly withdrawals).

get_times

get method for the product time-line. Returns a timeDate object

get_age

get method for the age of the insured

set_age

set method for the age of the insured

get_barrier

get method for the state-dependent fee barrier. Returns a positive scalar with the barrier

set_barrier

set method for the state-dependent fee barrier. Argument must be a positive scalar.

set_penalty_object

the argument penalty is a penalty_class object which is stored in a private field.

get_penalty_object

gets the penalty_class object.

set_penalty

set method for the penalty applied in case of surrender. The argument must be a scalar between 0 and 1.

get_penalty

get method for the surrender penalties. It can be a scalar between 0 and 1 in case the penalty is constant or a numeric vector in case the penalty varies with time.

set_fee

set method for the contract fee. The argument is a constant_parameters object with the fee.

set_payoff

set method for the payoff_guarantee object.

survival_benefit_times

returns a numeric vector with the survival benefit time indexes.

surrender_times

returns a numeric vector with the surrender time indexes. Takes as argument a string with the frequency of the decision if surrendering the contract, e.g. "3m" corresponds to a surrender decision taken every 3 months.

times_in_yrs

returns the product time-line in fraction of year

cash_flows

returns a numeric vector with the cash flows of the product. It takes as argument: spot_values a numeric vector which holds the values of the underlying fund, death_time a time index with the time of death and discounts a numeric vector with the discount factors at time of death. These latest are used to calculate the death benefit for the GMWB of type Wa

survival_benefit

Returns a numeric scalar corresponding to the survival benefit. The arguments are: spot_values vector which holds the values of the underlying fund, death_time time index of the time of death and time the time index of the survival benefit. The function will return 0 if there's no survival benefit at the specified time

get_premium

Returns the premium as non negative scalar

References

1. [BMOP2011] Bacinello A.R., Millossovich P., Olivieri A., Pitacco E., "Variable annuities: a unifying valuation approach." In: Insurance: Mathematics and Economics 49 (2011), pp. 285-297.

2. [BHM2014] Bernard C., Hardy M. and Mackay A. "State-dependent fees for variable annuity guarantees." In: Astin Bulletin 44 (2014), pp. 559-585.

Examples

# NOT RUN {
#Sets up the periodic payment.

premium <- 100
beta <- 0.1
GMWB_payment <- payoff_GMWB$new(premium, beta)

#Issue date of the contract
t0 <- timeDate::timeDate("2016-01-01")

#Ten years expiration of the guarantee

t1 <- timeDate::timeDate("2025-12-31")

age <- 60

# A constant fee of 2% per year (365 days)
fee <- constant_parameters$new(0.02)

#Barrier for a state-dependent fee. The fee will be applied only if
#the value of the account is below the barrier
barrier <- 200

#Withdrawal penalty applied in case the insured surrenders the contract
#It is a constant penalty in this case
penalty <- penalty_class$new(type = 1, 0.01)

#Sets up a VA contract with GMWB guarantee type Wa with yearly
#withdrawals for 10 years.

contract <- GMWB$new(GMWB_payment, t0 = t0, t1 = t1, age = age,  fee = fee,
barrier = barrier, penalty = penalty, type = "Wa", freq = "12m")

# }