Pricing of variable annuity life insurance
contracts by means of Monte Carlo methods. Monte Carlo is used to price
the contract in case the policyholder cannot surrender while
Least Squares Monte Carlo is used if the insured can surrender.
This package implements the pricing framework and algorithm described in
Bacinello et al. (2011)
Valuer aims at pricing a type of life insurance contract called variable annuity. The package implements the valuation framework and algorithms described in BMOP2011 where Monte Carlo methods are adapted to the life insurance case. It's written using R6 and comes with classes which describe the variable annuity contracts and other classes, called pricing engines, which are used to price those contracts.
The following code prices a 10 years VA with GMAB guarantee by means of a pricing engine which models the underlying fund as a geometric Brownian motion. Please check the introductory vignette for an explanation of this example and a description of the package structure.
library(valuer)#> Loading required package: orthopolynom#> Loading required package: polynomrate <- constant_parameters$new(0.01)premium <- 100rollup <- payoff_rollup$new(premium, rate)#Ten years time-linebegin <- timeDate::timeDate("2016-01-01")end <- timeDate::timeDate("2025-12-31")#Age of the policyholder.age <- 60# A constant fee of 4% per year (365 days)fee <- constant_parameters$new(0.04)#Barrier for a state-dependent fee. The fee will be applied only if#the value of the account is below the barrierbarrier <- Inf#Withdrawal penalty applied in case the insured surrenders the contract#It is a constant penalty in this casepenalty <- penalty_class$new(type = 1, 0.01)#Sets up the contract with GMAB guaranteecontract <- GMAB$new(rollup, t0 = begin, t = end, age = age, fee = fee, barrier = barrier, penalty = penalty)#Interest rater <- constant_parameters$new(0.03)#Initial value of the underlying fundspot <- 100#Volatilityvol <- constant_parameters$new(0.2)#Dividend ratediv <- constant_parameters$new(0.0)#Gatherer for the MC point estimatesthe_gatherer <- mc_gatherer$new()#Number of paths to simulateno_of_paths <- 1e3#Sets up the pricing engine specifying the va_contract, the interest rate#the parameters of the Weibull intensity of mortality, the initial fund#value, the volatility and dividends rateengine <- va_bs_engine$new(contract, r, c1=90.43, c2=10.36, spot,volatility=vol, dividends=div)#Estimates the contract value by means of the static approach.engine$do_static(the_gatherer, no_of_paths)the_gatherer$get_results()#> mean se#> 1 94.6241 1.155781
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