va_engine: Generic Variable Annuity pricing engine
In valuer: Pricing of Variable Annuities

Description Usage Format Value Methods References

Class providing an interface for a generic VA pricing engine.
This class shouldn't be instantiated but used as base class for variable annuity pricing engines. The value of the VA contract is estimated by means of the Monte Carlo method if the policyholder cannot surrender (the so called "static" approach), and by means of Least Squares Monte Carlo in case the policyholder can surrender the contract (the "mixed" approach).
See References -[BMOP2011] for a description of the mixed and static approaches and the algorithm implemented by this class, [LS2001] for Least Squares Monte Carlo.

va_engine

R6Class object.

Object of R6Class

new

Constructor method

death_time

Returns the time of death index. If the death doesn't occur during the product time-line it returns the last index of the product time-line plus one.

simulate_financial_paths

Simulates npaths paths of the underlying fund of the VA contract and the discount factors (interest rate) and saves them into private fields for later use.

simulate_mortality_paths

Simulates npaths paths of the intensity of mortality and saves them into private fields for later use.

get_fund

Gets the i-th path of the underlying fund where i goes from 1 to npaths

do_static

Estimates the VA contract value by means of the static approach (Monte Carlo), see References. It takes as arguments:

the_gatherer: gatherer object to hold the point estimates
npaths: positive integer with the number of paths to simulate
simulate: boolean to specify if the paths should be simulated from scratch, default is TRUE.

do_mixed

Estimates the VA contract by means of the mixed approach (Least Squares Monte Carlo), see References. It takes as arguments:

the_gatherer: gatherer object to hold the point estimates
npaths: positive integer with the number of paths to simulate
degree: positive integer with the maximum degree of the weighted Laguerre polynomials used in the least squares by LSMC
freq: string which contains the frequency of the surrender decision. The default is "3m" which corresponds to deciding every three months if surrendering the contract or not.
simulate: boolean to specify if the paths should be simulated from scratch, default is TRUE.

get_discount

Arguments are i,j. Gets the j-th discount factor corresponding to the i-th simulated path of the discount factors. This method must be implemented by sub-classes.

fair_fee

Calculates the fair fee for a contract using the bisection method. Arguments are:

fee_gatherer: data_gatherer object to hold the point estimates
npaths: numeric scalar with the number of MC simulations to run
lower: numeric scalar with the lower fee corresponding to positive end of the bisection interval
upper: numeric scalar with the upper fee corresponding to the negative end of the bisection interval
mixed: boolean specifying if the mixed method has to be used. The default is FALSE
tol: numeric scalar with the tolerance of the bisection algorithm. Default is 1e-4
nmax: positive integer with the maximum number of iterations of the bisection algorithm
simulate: boolean specifying if financial and mortality paths should be simulated.

[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.
[LS2001] Longstaff F.A. e Schwartz E.S. Valuing american options by simulation: a simple least-squares approach. In: Review of Financial studies 14 (2001), pp. 113-147

valuer documentation built on May 2, 2019, 3:43 p.m.