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.

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`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

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