GMWB: Variable Annuity with GMWB guarantee
In IvanZoccolan/valuer: Pricing of Variable Annuities

Description Usage Format Value Methods References Examples

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.

GMWB

R6Class object.

Object of R6Class

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

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

#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")