valuer (version 1.1.2)

va_pde_pricer: PDE Pricing of Variable Annuity

Description

va_pde_pricer returns the price of a VA with GMAB and GMDB guarantees. The underlying fund is a GBM and the intensity of mortality is deterministic. The fee has a state-dependent structure.

Usage

va_pde_pricer(F0 = 100, r = 0.03, sigma = 0.165, x = 50, delta = 0,
  fee = 0.01, beta = 150, T = 5, dt = 0.1, dF = 0.1,
  lambda = function(t) makeham(t, x = 50, A = 1e-04, B = 0.00035, c = 1.075),
  K = function(t, T) {     0.05 * (1 - t/T)^3 }, Fmax = 500)

Arguments

F0

numeric scalar with the initial value of the underlying fund

r

numeric scalar with the constant interest rate

sigma

numeric scalar with the constant volatility

x

numeric integer with the age of the insured

delta

numeric scalar with the roll-up rate of the GMAB and GMDB

fee

numeric scalar with the state-dependent base fee

beta

numeric scalar with the state-dependent barrier It should be greater than F0. If set to Inf the fee structure becomes constant

T

numeric integer with the maturity of the contract

dt

numeric scalar with the discretization step of the time dimension

dF

numeric scalar with the discretization step for the fund dimension

lambda

function with the intensity of mortality. Default is makeham with parameters x = 50, A = 0.0001, B = 0.00035, c = 1.075

K

function with the surrender penalty.

Fmax

numeric scalar with the maximum fund value

Value

numeric scalar with the VA price

Details

This function resolves the PDE in [MK2017] by means of the finite difference implicit method. It requires the package limSolve to be installed.

References

1. [MK2017] A. MacKay, M. Augustyniak, C. Bernard, and M.R. Hardy. Risk management of policyholder behavior in equity-linked life insurance. The Journal of Risk and Insurance, 84(2):661-690, 2017. DOI: 10.1111/jori.12094

Examples

# NOT RUN {
lambda <- function(t) mu(t, x = 50, c1 = 90.43 , c2 = 10.36)
K <- function(t, T) {0.05 * ( 1 - t / T)^3}

va <- va_pde_pricer(lambda = lambda, K = K, Fmax = 200)

va
# }